Description
Functional Analysis develops the theory of functional analysis through a rigorous treatment of topological vector spaces, Banach spaces, Hilbert spaces, and linear operators. The book covers completeness, convexity, the Hahn–Banach theorems, weak topologies, duality, compactness, spectral theory, and operator algebras, with attention to important results such as the Banach–Steinhaus, open mapping, and closed graph theorems. It also discusses applications involving vector-valued integration, holomorphic functions, fixed-point theory, invariant subspaces, and ergodic theory. The second edition includes additional examples and exercises, making the text suitable for advanced study and graduate-level courses in functional analysis.
