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Function Spaces

  • Irving E. Segal
  • Ray A. Kunze
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 228)

Abstract

In the case of a finite-dimensional linear space L, the dual, or conjugate, space L* consisting of all linear functionals on L plays an important role in the general theory. The primary result in the finite-dimensional case is that the natural injection of L into the dual L** of L is an isomorphism of L onto L**. This means that if x is an element of L and x** denotes the element of L** given by the equation x**(f) = f(x) for all f in L*, then the map xx** is one-to-one from L onto L**.

Keywords

Banach Space Measure Space Linear Functional Weak Topology Continuous Linear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Irving E. Segal
    • 1
  • Ray A. Kunze
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.University of California at IrvineIrvineUSA

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