Invertibility and Singularity for Bounded Linear Operators PDF Download

Author: Robin Harte
Publisher: Courier Dover Publications
ISBN: 0486810305
Category : Mathematics
Languages : en
Pages : 627

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Originally published: New York: Marcel Dekker, Inc., 1988.

Author: Dragana S. Cvetković Ilić
Publisher: American Mathematical Society
ISBN: 1470469871
Category : Mathematics
Languages : en
Pages : 170

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Book Description
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.

Author: Carlos S. Kubrusly
Publisher: Springer Nature
ISBN: 3030331490
Category : Mathematics
Languages : en
Pages : 257

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Book Description
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.

Author: Robin Harte
Publisher: Springer Nature
ISBN: 3031139178
Category : Mathematics
Languages : en
Pages : 193

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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

Author: Vladimir Müller
Publisher: Birkhäuser
ISBN: 3034877889
Category : Mathematics
Languages : en
Pages : 390

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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.

Author: Dragana S. Cvetković‐Ilić
Publisher: Springer
ISBN: 9811063494
Category : Mathematics
Languages : en
Pages : 203

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Book Description
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.

Author: VV.AA.
Publisher: Ed. Universidad de Cantabria
ISBN: 9788487412400
Category : Mathematics
Languages : en
Pages : 308

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Author: Ronald Cross
Publisher: CRC Press
ISBN: 9780824702199
Category : Mathematics
Languages : en
Pages : 356

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Book Description
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.

Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 1599731282
Category :
Languages : en
Pages : 139

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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.

Author: Carlos S. Kubrusly
Publisher: Springer Science & Business Media
ISBN: 0817683283
Category : Mathematics
Languages : en
Pages : 203

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Book Description
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. ​