Essential Results of Functional Analysis

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, provides a complete and concise presentation of the fundamental ideas and theorems of functional analysis. It introduces essential notions and results from various areas of mathematics where functional analysis plays a crucial role, demonstrating the unity of perspective and technique that this approach offers. Zimmer covers a wide range of topics, including convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. The book emphasizes the direct presentation of central theorems and the structural framework needed to understand them, making it an invaluable resource for both mathematics and physics students and researchers.