Download or read book Lipschitz Algebras Second Edition written by Nik Weaver and published by World Scientific. This book was released on 2018-05-14 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is very well-written by one of the leading figures in the subject. It is self-contained, includes relevant recent advances and is enriched by a large number of examples and illustrations. In addition to the general bibliography, each chapter includes a section of notes, which details the authorship of the main results, and provides useful hints for further readings. Undoubtedly, this edition will be received by researchers with the same success as the first one.'European Mathematical SocietyThis is the standard reference on algebras of Lipschitz functions, written by the leading figure in the field. The second edition includes new chapters on nonlinear Banach space geometry, differentiability in metric measure spaces, and quantum metrics. This latest material reflects the importance of spaces of Lipschitz functions in a diverse range of current research directions. Every functional analyst should have some knowledge of this subject.
Download or read book Lipschitz Algebras written by Nik Weaver and published by World Scientific. This book was released on 1999-07-22 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lipschitz algebras Lip(M), for M a complete metric space, are quite analogous to the spaces C(Ω) and L∞(X), for Ω a compact Hausdorff space and X a σ-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Download or read book Lipschitz Algebras written by Nik Weaver and published by World Scientific. This book was released on 1999 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Download or read book Automatic Continuity of Lipschitz Algebras written by Branka Pavloviic and published by . This book was released on 1993 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lipschitz Functions written by Ştefan Cobzaş and published by Springer. This book was released on 2019-05-23 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Download or read book Extension Problems and Stable Ranks written by Raymond Mortini and published by Springer Nature. This book was released on 2021-08-02 with total page 2197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained encyclopedic monograph gives a detailed introduction to Bézout equations and stable ranks, encompassing and explaining needed topological, analytical, and algebraic tools and methods. Some of the highlights included are Carleson's corona theorem and the Bass, topological, and matricial stable ranks. The first volume focusses on topological structures, Banach algebras, and advanced function theory, thus preparing the stage for the algebraic structures in the second volume towards examining stable ranks with analytic methods. The main emphasis is laid on algebras of holomorphic functions. Often a new approach is presented or at least a different angle of sight, which makes the book attractive both for researchers and students interested in these active fields of research.
Download or read book Associative and Non Associative Algebras and Applications written by Mercedes Siles Molina and published by Springer Nature. This book was released on 2020-01-02 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.
Download or read book Banach Function Algebras Arens Regularity and BSE Norms written by Harold Garth Dales and published by Springer Nature. This book was released on with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A von Neumann Algebra Approach to Quantum Metrics Quantum Relations written by Greg Kuperberg and published by American Mathematical Soc.. This book was released on 2012 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.
Download or read book Mathematical Quantization written by Nik Weaver and published by CRC Press. This book was released on 2001-05-31 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a
Download or read book Bornologies and Lipschitz Analysis written by Gerald Beer and published by CRC Press. This book was released on 2023-05-15 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology. Special attention is given to Lipschitz and locally Lipschitz functions. For example, uniformly dense subclasses of locally Lipschitz functions within the real-valued continuous functions, Cauchy continuous functions, and uniformly continuous functions are presented. It is shown very generally that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by a real-valued Lipschitz function, the composition has the property. Bornological convergence of nets of closed subsets, having Attouch-Wets convergence as a prototype, is considered in detail. Topologies of uniform convergence for continuous linear operators between normed spaces is explained in terms of the bornological convergence of their graphs. Finally, the idea of a bornological extension of a topological space is presented, and all regular extensions can be so realized.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1969 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Spaces written by K. Jarosz and published by CRC Press. This book was released on 1995-07-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the proceedings from the Second Conference on Function Spaces, this work details known results and fresh discoveries on a wide range of topics concerning function spaces. It covers advances in areas such as spaces and algebras of analytic functions, Lp-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.
Download or read book Nigel J Kalton Selecta written by Fritz Gesztesy and published by Birkhäuser. This book was released on 2016-07-05 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it. Nigel Kalton (1946-2010) was an extraordinary mathematician who made major contributions to an amazingly diverse range of fields over the course of his career.
Download or read book Recent Developments in Fractal Geometry and Dynamical Systems written by Sangita Jha and published by American Mathematical Society. This book was released on 2024-04-18 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.
Download or read book The Mathematical Legacy of Victor Lomonosov written by Richard M. Aron and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-10 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside's theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1996-09 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
