Description
Book SynopsisIntroduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators.
Trade Review“This book contains a wealth of material. Each chapter concludes with a comprehensive set of exercises that serve to illustrate the theory. Solutions to the exercises are given in the final section.” -- Mathematical Reviews
Table of ContentsHilbert spaces and basic operator theory: Linear spaces; normed spaces; first examples Hilbert spaces The dual space Bounded linear operators Spectrum. Fredholm theory of compact operators Self-adjoint operators Functions of operators; spectral decomposition Basics of functional analysis: Spectral theory of unitary operators The fundamental theorems and the basic methods Banach algebras Unbounded self-adjoint and symmetric operators in $H$ Solutions to exercises Bibliography Symbols index Subject index.
