Contents: Metric spaces; Spaces of functions; Hilbert spaces; Banach spaces; Applications of Banach space ideas to Fourier series; operators on Hilbert space; spectral theorem for self-adjoint compact operators on Hilbert spaces; topological vector spaces; categorical constructions; vector-valued integrals; Banach-Alaoglu, variant Banach-Steinhaus, bipolars, weak-to-strong principles; vector-valued holomorphic functions, weak-to-strong holomorphy; Measurable choice functions ; Schwartz-function envelopes of rapidly decreasing; Weak smoothness implies strong smoothness; Uniqueness of invariant distributions; Hahn-Banach theorems; Catalogue of topological vector spaces; Distribution-theoretic proof of Poisson Summation Formula; A good spectral theorem; Bernstein's analytic continuation of complex powers of polynomials. |