Titlebook: Topological Vector Spaces; Helmut H. Schaefer Textbook 19711st edition Springer Science+Business Media New York 1971 Finite.Manifold.Morph

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Linear Mappings,ccent in this chapter is on vector spaces whose elements are vector-valued functions, especially linear mappings. The study of such spaces and their topologies forms the natural background for much of what follows in this book, in particular, duality (Chapter IV) and spectral theory (Appendix); it a

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Order Structures,o give an account of the extensive literature on Banach lattices, for a survey of which we refer the reader to Day [2], nor is any special emphasis placed on ordered normed spaces. Our efforts are directed towards developing a theory that is in conformity with the modern theory of topological vector

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Locally Convex Topological Vector Spaces,ield ., where either . = . or . = .. If . = ., . . be considered a subfield and restriction of scalars to . . be indicated by the use of the adjective “ real ” (Chapter I, Section 7). In particular, the symbols > and ≧, when used between scalars, refer to the customary order in .; for example, “λ > 0” means “λ ∈ . and λ.0”.

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Linear Mappings,opologies forms the natural background for much of what follows in this book, in particular, duality (Chapter IV) and spectral theory (Appendix); it also leads, via spaces of bilinear maps and topological tensor products, to the important class of nuclear spaces.

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https://doi.org/10.1007/978-1-4684-9928-5Finite; Manifold; Morphism; Spaces; Vector; algebra; approximation; duality; function; graph; mathematics; proo