Designed for students of probability and stochastic processes, as well as for students of functional analysis, specifically, this volume presents some chosen parts of functional analysis that can help clarify probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.

Adam Bobrowski is a Professor of Mathematics at Lublin University.

Preface; 1. Preliminaries, notations and conventions; 2. Basic notions in functional analysis; 3. Conditional expectation; 4. Brownian motion and Hilbert spaces; 5. Dual spaces and convergence of probability measures; 6. The Gelfand transform and its applications; 7. Semigroups of operators and Lévy processes; 8. Markov processes and semigroups of operators; 9. Appendixes; References; Index.