Functional Analysis: An Introduction
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This text supports two semester-length courses. The first covers Hilbert spaces and basic operator theory, with sections on linear, normed, and Hilbert spaces and the dual space, bounded linear operators, spectrum, the Fredholm theory of compact operators, self- adjoint operators, functions of operators, and spectral decomposition. This material requires only a first course in linear algebra as a prerequisite. The second course covers the basics of functional analysis, with sections on fundamental theorems and basic methods, spectral theory of unitary operators, Banach algebras, and unbound self-adjoint and symmetric operators in H. This course requires a background in measure theory. Each section includes exercises with solutions in the appendix. Annotation ©2004 Book News, Inc., Portland, OR
1Linear spaces; normed spaces; first examples32Hilbert spaces253The dual space474Bounded linear operators555Spectrum. : Fredholm theory of compact operators756Self-adjoint operators877Functions of operators; spectral decomposition1058Spectral theory of unitary operators1219The fundamental theorems and the basic methods12710Banach algebras16711Unbounded self-adjoint and symmetric operators in H203
