Volumes I through V of Theorems and Problems in Functional Analysis: The Answer Book present different techniques for solving the 828 Exercises found in the A.A. Kirillov and Gvichiani book, entitled Theorems and Problems in Functional Analysis. The original book by Kirillov and Gvichiani was in the Problem Book in Mathematics Series, published by Springer.

This volume focuses on the Spectral theory of operators.  The key topics covered are:

-functional calculus,

-the Jordan matrices,

-auto-adjoint operators,

-the Volterra operator,

-Spectral decomposition of the operators,

-reduction of an operator,

-the Spectral theorem,

-the Weyl criterion,

-the Stone formula, and

-the Von Neumann Ergodic theorem.

Supplementing the book, Theorems and Problems in Functional Analysis, these volumes may be used by graduate students taking a course in functional analysis.  In order to understand this text, the reader must be familiar with mathematical analysis and real analysis.