Topological Vector Spaces
Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate.
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n LOCALLY CONVEX TOPOLOGICAL
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adjoint algebraic assertion Banach lattice Banach space barreled space bilinear bounded sets bounded subsets called canonical imbedding canonical map canonical order Chapter circled hull circled O-neighborhood circled subset closed subspace closure compact space compact subset contains continuous linear form continuous linear map convex hull corollary countable defined denote dense direct sum duality elements equicontinuous equicontinuous subsets equivalent example Exercise exists F)-space family of bounded filter finite subset follows functions Hausdorff t.v.s. hence Hilbert space hyperplane implies inductive limit isomorphism l.c. topology lemma Let F locally convex space locally convex topology metrizable non-empty normal cone normed space nuclear spaces null sequence O-neighborhood base order complete ordered vector space positive cone positive linear form precompact projective topology properties quasi-complete reflexive respectively S-topology Section semi-norms semi-reflexive spectral strong dual subspace summable theorem topology of simple vector lattice