Format:
1 Online-Ressource (XII, 249 p. 2 illus.)
ISBN:
9783030331498
Series Statement:
Springer eBook Collection
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783030331481
Additional Edition:
ISBN 9783030331504
Additional Edition:
ISBN 9783030331511
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030331481
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030331504
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030331511
Language:
English
Keywords:
Operatortheorie
;
Funktionalanalysis
;
Spektrum
;
Linearer Operator
DOI:
10.1007/978-3-030-33149-8
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