This classic textbook introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
Here's a sample of other books in this Dover category
Functional Analysis by Frigyes Riesz, Béla Sz.-Nagy Classic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.
Hardy Classes by Marvin Rosenblum, James Rovnyak Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Includes general theory of shift operators on a Hilbert space, more. Appendix. Bibliography. 1985 edition.
Invariant Subspaces by Heydar Radjavi, Peter Rosenthal Broad survey focuses on operators on separable Hilbert spaces. Topics include normal operators, analytic functions of operators, shift operators, invariant subspace lattices, compact operators, invariant and hyperinvariant subspaces, more. 1973 edition.
Theory of Linear Operations by Stefan Banach, F. Jellett Written by the founder of functional analysis, this is the first text on linear operator theory. Additional topics include the calculus of variations and theory of integral equations. 1987 edition.
Introduction to Spectral Theory in Hilbert Space by Gilbert Helmberg This introduction to Hilbert space, bounded self-adjoint operators, the spectrum of an operator, and operators' spectral decomposition is accessible to readers familiar with analysis and analytic geometry. 1969 edition.
Unbounded Linear Operators: Theory and Applications by Seymour Goldberg In simple notation and a readable style, this classic offers advanced undergraduates and graduate students a comprehensive, self-contained, and systematic treatment covering both theory and applications to differential equations.
