Function Spaces

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


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**.


Banach Space Measure Space Linear Functional Weak Topology Continuous Linear 
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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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