Abstract
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.
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References to Chapter X
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Gross, H. (1979). Extension of Isometries. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3542-7_11
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DOI: https://doi.org/10.1007/978-1-4899-3542-7_11
Publisher Name: Birkhäuser, Boston, MA
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