Extension of Isometries

  • Herbert Gross
Part of the Progress in Mathematics book series (PM, volume 1)


The main result in this chapter is a theorem in [1] on the extension of isometries φ: V → V̄ between ⊥-closed subspaces of a sesquilinear space E (Theorems 5 and 9 below). The crucial assumptions for an extension to exist turn out to be equality of the isometry types of V and V-⊥ and homeomorphy of V and V under φ with respect to the weak linear topology σ(Φ) attached to the form on E.


Closed Subspace Dual Pair Isotropic Subspace Quotient Topology Linear Topology 
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References to Chapter X

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    W. Allenspach, Erweiterung von Isometrien in alternierenden Räumen. Ph. D. Thesis, University of Zurich 1973.Google Scholar
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Herbert Gross
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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