The notion of linear mapping has been used frequently before and is obviously indispensable for any discussion of topological vector spaces. But the accent 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 also leads, via spaces of bilinear maps and topological tensor products, to the important class of nuclear spaces.
KeywordsBanach Space Convex Space Null Sequence Nuclear Space Baire Space
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