Spectral Theory of Bounded Linear Operators

ISBN-13: 9783030331481 / Angielski / Twarda / 2020 / 249 str.

Carlos S. Kubrusly

Opis

Here is a concise introduction to spectral theory of Hilbert space operators. It presents recent theoretical aspects and features detailed proofs. The coverage of topics is thorough and explores various delicate points and hidden features often left untreated.

Recenzje

"The exposition of this book is clear and structured. ... A rich bibliography comprising 114 entries is provided. The book is addressed to graduate researchers interested in the spectral theory for bounded linear operators." (Bilel Krichen, zbMATH 1454.47001, 2021)

Spis treści

Preface.- Introductory Results.- Spectrum of an Operator.- The Spectral Theorem.- Functional Calculi.- Fredholm Theory in Hilbert Space.- Aspects of Fredholm Theory in Banach Space.- A Glimpse at Multiplicity Theory.

O autorze

Carlos Kubrusly is Emeritus Professor at Catholic University of Rio de Janeiro. His research focuses on operator theory, particularly on weak and strong dynamics of Hilbert-space operators and their connection with the Invariant Subspace Problem. He has published over 100 scientific articles in international journals, five books, and served as the editor-in-chief of the journal Computational and Applied Mathematics.

Blurb

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.