Introductory Theory of Topological Vector Spaces

Description

Content: Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface 1: Hahn-Banach's extension theorem 2: Banach spaces and Hilbert spaces 3: Operators and some consequences of Hahn-Banach's extension theorem 4: The uniform boundedness theorem and Banach's open mapping theorem 5: A structure theorem for compact sets in a Banach space 6: Topological injections and topological surjections 7: Vector topologies 8: Separation theorems and Krein-Milman's theorem 9: Projective topologies and inductive topologies 10: Normed spaces associated with a locally convex space 11: Bounded sets and compact sets in metrizable topological vector spaces12: The bornological space associated with a locally convex space 13: Vector bornologies 14: Initial bornologies and final bornologies 15: von Neumann bornologies and locally convex topologies determined by convex bornologies 16: Dual pairs and the weak topology 17: Elementary duality theory 18: Semi-reflexive spaces and ultra-semi-reflexive spaces 19: Some recent results on compact operators and weakly compact operators 20: Precompact seminorms and Schwartz spaces 21: Elementary Riesz-Schauder's theory 22: An introduction to operator ideals23: An aspect of fixed point theory 24: An introduction to ordered convex spaces Special symbols References Index