Download or read book Invertibility and Singularity for Bounded Linear Operators written by Robin Harte and published by Courier Dover Publications. This book was released on 2016-11-16 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for courses in functional analysis and a valuble resource for researchers, this introductory treatment is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. 1988 edition.
Download or read book Invertibility and Singularity for Bounded Linear Operators written by Robin Harte and published by Courier Dover Publications. This book was released on 2016-10-20 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Marcel Dekker, Inc., 1988.
Download or read book Fredholm and Invertible Tuples of Bounded Linear Operators written by Raul Enrique Curto and published by . This book was released on 1978 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Inverses and Applications written by University of Wisconsin--Madison. Mathematics Research Center and published by . This book was released on 1976 with total page 1082 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics on Invertibility of Linear Operators written by Kerry Gail Brock and published by . This book was released on 1988 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Completion Problems on Operator Matrices written by Dragana S. Cvetković Ilić and published by American Mathematical Society. This book was released on 2022-06-07 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.
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 249 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 Spectral Computations for Bounded Operators written by Mario Ahues and published by CRC Press. This book was released on 2001-02-26 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for
Download or read book Spectral Mapping Theorems written by Robin Harte and published by Springer Nature. This book was released on 2023-04-03 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first. Starting with a summary of the basic algebraic systems – semigroups, rings and linear algebras – the book quickly turns to topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Key aspects of spectral theory are covered, in one and several variables. Finally the case of an arbitrary set of variables is discussed. Spectral Mapping Theorems is an accessible and easy-to-read guide, providing a convenient overview of the topic to both students and researchers. From the reviews of the first edition "I certainly plan to add it to my own mathematical library" — Anthony Wickstead in the Irish Mathematical Society Bulletin "An excellent read" — Milena Stanislavova in the Mathematical Reviews "[Offers] a fresh perspective even for experts [...] Recommended" — David Feldman in Choice
Download or read book Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras written by Vladimir Müller and published by Birkhäuser. This book was released on 2013-11-11 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
Download or read book Invertibility Positive Linear Operators on Spaces of Continuous Functions written by Rand Corporation and published by . This book was released on 1965 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Properties of Generalized Inverses written by Dragana S. Cvetković‐Ilić and published by Springer. This book was released on 2017-10-07 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.
Download or read book Aportaciones matem ticas written by VV.AA. and published by Ed. Universidad de Cantabria. This book was released on 1991 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivalued Linear Operators written by Ronald Cross and published by CRC Press. This book was released on 1998-07-09 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructs a theoretical framework for the study of linear relations and provides underlying concepts, rules, formulae, theorems and techniques. The book compares the inversion, adjoints, completion and closure of various classes of linear operators. It highlights compact and precompact relations.
Download or read book The Singular Value Expansion for Compact and Non compact Operators written by and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract : Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, A, μ) and isometries V : L2(M) X→, U : L2(M) → Y and a nonnegative, bounded, measurable function (sigma) : M → [0, ∞) such that T = Um(sigma)V †, with m(sigma) : L2(M ) → L2(M ) defined by m(sigma)(f ) = (sigma)f for all f ∈ L2(M ). The expansion T = Um(sigma)V † is called the singular value expansion (SVE) of T . The SVE is a useful tool for analyzing a number of problems such as the computation of the generalized inverse T† of T , understanding the inverse problem Tx = y and, regularizing Tx = y using methods such as Tikhonov regularization. In fact, many standard Tikhonov regularization results can be derived by making use of the SVE. The expansion T = Um(sigma)V † can also be compared to the SVE of a compact operator T : X → Y which has the form T = (sigma)nun ⊗ vn where the above sum may be finite or infinite depending on the rank of T . The set {(sigma)n} is a sequence of positive real numbers that converge to zero if T has infinite rank. Such (sigma)n are the singular values of T . The sets {vn} ⊂ X and {un} ⊂ Y are orthonormal sets of vectors that satisfy Tvn = (sigma)nun for all n. The vectors vn and un are the right and left singular vectors of T, respectively. If the essential range, denoted Ress(sigma), forms a sequence of positive real numbers converging to zero (or is merely a finite set of nonnegative real numbers) and for each nonzero s ∈ Ress(sigma), the essential preimage of the singleton set s , denoted (sigma)ess−1( {s} ), is finite, then the bounded operator T = Ums(sigma)V † is in fact compact. The converse of this statement is also true. If the operator T is compact, the singular values and vectors of T may be approximated by discretizing the operator and finding the singular value decomposition of a scaled Galerkin matrix. In general, the approximated singular values and vectors converge at the same rate, which is governed by the error (in the operator norm) in approximating T by the discretized operator. However, when the discretization is accomplished by projection (variational approximation), the computed singular values converge at an increased rate; the typical case is that the errors in the singular values are asymptotically equal to the square of the errors in the singular vectors (this statement must be modified if the approximations to the left and right singular vectors converge at different rates). Moreover, in the case of variational approximation, the error in the singular vectors can be compared with the optimal approximation error, with the two being asymptotically equal in the typical case.
Download or read book Advanced Functional Analysis written by Eberhard Malkowsky and published by CRC Press. This book was released on 2019-02-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research
Download or read book Scientia Magna Vol 6 No 2 2010 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache's Orthic Theorem, Smarandache's Concurrent Lines Theorem, character graph in Brauer graph's model, robust stability of switched linear systems with time-varying delay, majority neighborhood number of a graph, divisibility tests for Smarandache semigroups, Hopf bifurcation in a predator-prey model with distributed delays, and similar topics. Contributors: R. S. Maragatham, S. Asawasamarit, U. Leerawat, S. Balasubramanian, D. Senthilkumar, M. Khoshnevisan, D. Senthilkumar, Sherinjoy S. M., and others.
