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Spectral Theory of Bounded Linear Operators (Hardcover, 1st ed. 2020)
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Spectral Theory of Bounded Linear Operators (Hardcover, 1st ed. 2020)
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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.
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