Linear Mappings

  • Helmut H. Schaefer
Part of the Graduate Texts in Mathematics book series (GTM, volume 3)


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.


Banach Space Convex Space Null Sequence Nuclear Space Baire Space 
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    Brace,.J. W. The topology of almost uniform convergence. Pacific J. Math., 9 (1959), 643–652.MathSciNetMATHGoogle Scholar
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    Brace,.J. W. Approximating compact and weakly compact operators. Proc. Amer. Math. Soc., 12 (1961), 392–393.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York 1971

Authors and Affiliations

  • Helmut H. Schaefer
    • 1
  1. 1.University of TübingenGermany

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