Download or read book Spectral Theory of Hyponormal Operators written by Xia and published by Birkhäuser. This book was released on 2013-11-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral analysis of linear operators has always been one of the more active and important fields of operator theory, and of extensive interest to many operator theorists. Its devel opments usually are closely related to certain important problems in contemporary mathematics and physics. In the last 20 years, many new theories and interesting results have been discovered. Now, in this direction, the fields are perhaps wider and deeper than ever. This book is devoted to the study of hyponormal and semi-hyponormal operators. The main results we shall present are those of the author and his collaborators and colleagues, as well as some concerning related topics. To some extent, hyponormal and semi-hyponormal opera tors are "close" to normal ones. Although those two classes of operators contain normal operators as a subclass, what we are interested in are, naturally, nonnormal operators in those classes. With the well-studied normal operators in hand, we cer tainly wish to know the properties of hyponormal and semi-hypo normal operators which resemble those of normal operators. But more important than that, the investigations should be concen trated on the phenomena which only occur in the nonnormal cases.
Download or read book Spectral Theory of Hyponormal Operators written by Daoxing Xia and published by Birkhäuser. This book was released on 1983 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral analysis of linear operators has always been one of the more active and important fields of operator theory, and of extensive interest to many operator theorists. Its devel opments usually are closely related to certain important problems in contemporary mathematics and physics. In the last 20 years, many new theories and interesting results have been discovered. Now, in this direction, the fields are perhaps wider and deeper than ever. This book is devoted to the study of hyponormal and semi-hyponormal operators. The main results we shall present are those of the author and his collaborators and colleagues, as well as some concerning related topics. To some extent, hyponormal and semi-hyponormal opera tors are "close" to normal ones. Although those two classes of operators contain normal operators as a subclass, what we are interested in are, naturally, nonnormal operators in those classes. With the well-studied normal operators in hand, we cer tainly wish to know the properties of hyponormal and semi-hypo normal operators which resemble those of normal operators. But more important than that, the investigations should be concen trated on the phenomena which only occur in the nonnormal cases.
Download or read book Spectral Theory of Hyponormal Operators written by Xia and published by Birkhäuser. This book was released on 2014-04-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral analysis of linear operators has always been one of the more active and important fields of operator theory, and of extensive interest to many operator theorists. Its devel opments usually are closely related to certain important problems in contemporary mathematics and physics. In the last 20 years, many new theories and interesting results have been discovered. Now, in this direction, the fields are perhaps wider and deeper than ever. This book is devoted to the study of hyponormal and semi-hyponormal operators. The main results we shall present are those of the author and his collaborators and colleagues, as well as some concerning related topics. To some extent, hyponormal and semi-hyponormal opera tors are "close" to normal ones. Although those two classes of operators contain normal operators as a subclass, what we are interested in are, naturally, nonnormal operators in those classes. With the well-studied normal operators in hand, we cer tainly wish to know the properties of hyponormal and semi-hypo normal operators which resemble those of normal operators. But more important than that, the investigations should be concen trated on the phenomena which only occur in the nonnormal cases.
Download or read book Spectral Theory of Operators on Hilbert Spaces written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-06-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field.
Download or read book Fredholm and Local Spectral Theory with Applications to Multipliers written by Pietro Aiena and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
Download or read book Spectral Theory of Bounded Linear Operators written by Carlos S. Kubrusly and published by Springer Nature. This book was released on 2020-01-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.
Download or read book Fredholm and Local Spectral Theory II written by Pietro Aiena and published by Springer. This book was released on 2018-11-24 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.
Download or read book An Introduction to Local Spectral Theory written by K. B. Laursen and published by Oxford University Press. This book was released on 2000 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Download or read book Notes on Spectral Theory written by Sterling K. Berberian and published by . This book was released on 1966 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Models and Decompositions in Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 1997-08-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.
Download or read book Analytic Theory Of Subnormal Operators written by Daoxing Xia and published by World Scientific. This book was released on 2014-12-18 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains an important progress on the theory of subnormal operators in the past thirty years, which was developed by the author and his collaborators. It serves as a guide and basis to students and researchers on understanding and exploring further this new direction in operator theory. The volume expounds lucidly on analytic model theory, mosaics, trace formulas of the subnormal operators, and subnormal tuples of operators on the Hilbert spaces.
Download or read book Spectral Theory of Block Operator Matrices and Applications written by Christiane Tretter and published by Imperial College Press. This book was released on 2008 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
Download or read book Hilbert Space Operators written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.
Download or read book Multivariable Operator Theory written by Ernst Albrecht and published by Springer Nature. This book was released on 2024-01-22 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Jörg Eschmeier made a number of fundamental contributions to the development of operator theory and related topics. The chapters in this volume, compiled in his memory, are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Download or read book Well Posedness of Parabolic Difference Equations written by A. Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Download or read book New Aspects in Interpolation and Completion Theories written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter polation conditions appear from two sides. The state space theory of time varying systems play an important role.
Download or read book One Dimensional Linear Singular Integral Equations written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.
