Birkhoff James Orthogonality And Geometry Of Operator Spaces

Author : Arpita Mal
Publisher : Springer Nature
ISBN 13 : 981997111X
Total Pages : 258 pages
Book Rating : 4.14/5 ( download)

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Download or read book Birkhoff-James Orthogonality and Geometry of Operator Spaces written by Arpita Mal and published by Springer Nature. This book was released on 2024 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of BirkhoffJames orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.

Author : Arpita Mal
Publisher : Springer
ISBN 13 : 9789819971107
Total Pages : 0 pages
Book Rating : 4.01/5 ( download)

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Download or read book Birkhoff–James Orthogonality and Geometry of Operator Spaces written by Arpita Mal and published by Springer. This book was released on 2023-12-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an insight into the geometric aspects of the spaces of operators studied by using the notion of Birkhoff–James orthogonality. It studies the norm attainment set of an operator and its properties, the notion of which plays a very important role in the characterization of B-J orthogonality of operators. The structure of the norm attainment set is studied for Hilbert space operators and is yet to be understood completely for operators between Banach spaces. The book explores the interrelation between B-J orthogonality in the ground space and in the space of operators in its fullest generality. The book further explores the concept of approximate B-J orthogonality and investigated its geometry both in the ground space as well as in the space of operators. It highlights important geometric properties like smoothness and k-smoothness of bounded linear operators, extreme contractions and symmetricity of bounded linear operators defined between Hilbert spaces as well as Banach spaces.

Author : Michael Ruzhansky
Publisher : CRC Press
ISBN 13 : 1351142100
Total Pages : 338 pages
Book Rating : 4.06/5 ( download)

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Download or read book Advanced Topics in Mathematical Analysis written by Michael Ruzhansky and published by CRC Press. This book was released on 2019-01-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

Author : John von Neumann
Publisher : Princeton University Press
ISBN 13 : 1400882257
Total Pages : 116 pages
Book Rating : 4.50/5 ( download)

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Download or read book Functional Operators (AM-22), Volume 2 written by John von Neumann and published by Princeton University Press. This book was released on 2016-03-02 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measures and integrals

Author : M. Amélia Bastos
Publisher : Springer Nature
ISBN 13 : 3030519457
Total Pages : 654 pages
Book Rating : 4.52/5 ( download)

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Download or read book Operator Theory, Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Author : Erik Magnus Alfsen
Publisher : Birkhauser
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.79/5 ( download)

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Download or read book Geometry of State Spaces of Operator Algebras written by Erik Magnus Alfsen and published by Birkhauser. This book was released on 2003 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete and self-contained solution to the long-standing problem of giving a geometric description of state spaces of C*-algebras and von Neumann algebras, and of their Jordan algebraic analogs (JB-algebras and JBW-algebras). This material, which has previously only appeared in research papers based on substantial prerequisites, is made accessible to a broad mathematical audience. The necessary prerequisites on C*-algebras and von Neumann algebras are summarized in an appendix, which contains all relevant definitions and results. All necessary background on Jordan algebras is given in the present book, and the first part of the book may be of independent interest for those wanting a quick introduction to Jordan algebras. This work will be of interest to researchers and students in operator algebras.

Author : Amir
Publisher : Birkhäuser
ISBN 13 : 3034854870
Total Pages : 205 pages
Book Rating : 4.70/5 ( download)

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Download or read book Characterizations of Inner Product Spaces written by Amir and published by Birkhäuser. This book was released on 2013-11-21 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematician working in Banaeh spaee geometry or Approximation theory knows, from his own experienee, that most "natural" geometrie properties may faH to hold in a generalnormed spaee unless the spaee is an inner produet spaee. To reeall the weIl known definitions, this means IIx 11 = *, where is an inner (or: scalar) product on E, Le. a function from ExE to the underlying (real or eomplex) field satisfying: (i) O for x o. (ii) is linear in x. (iii) = (intherealease, thisisjust =

Author : Gilles Pisier
Publisher : American Mathematical Soc.
ISBN 13 : 0821807102
Total Pages : 166 pages
Book Rating : 4.01/5 ( download)

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Download or read book Factorization of Linear Operators and Geometry of Banach Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.

Author : Richard M. Aron
Publisher : Springer Nature
ISBN 13 : 3031021045
Total Pages : 822 pages
Book Rating : 4.46/5 ( download)

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Download or read book Operator and Norm Inequalities and Related Topics written by Richard M. Aron and published by Springer Nature. This book was released on 2022-08-10 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

Author : Janusz Brzdęk
Publisher : Springer Nature
ISBN 13 : 3030289729
Total Pages : 514 pages
Book Rating : 4.20/5 ( download)

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Download or read book Ulam Type Stability written by Janusz Brzdęk and published by Springer Nature. This book was released on 2019-10-29 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in particular on the stability of many functional equations in a single and several variables (also in the lattice environments, Orlicz spaces, quasi-b-Banach spaces, and 2-Banach spaces) and some orthogonality relations (e.g., of Birkhoff–James). A variety of approaches are presented, but a particular emphasis is given to that of fixed points, with some new fixed point results and their applications provided. Besides these several other topics are considered that are somehow related to the Ulam stability such as: invariant means, geometry of Banach function modules, queueing systems, semi-inner products and parapreseminorms, subdominant eigenvalue location of a bordered diagonal matrix and optimal forward contract design for inventory. New directions and several open problems regarding stability and non-stability concepts are included. Ideal for use as a reference or in a seminar, this book is aimed toward graduate students, scientists and engineers working in functional equations, difference equations, operator theory, functional analysis, approximation theory, optimization theory, and fixed point theory who wish to be introduced to a wide spectrum of relevant theories, methods and applications leading to interdisciplinary research. It advances the possibilities for future research through an extensive bibliography and a large spectrum of techniques, methods and applications.