Isometries of Hilbert C*-modules

2001/04/19 by Baruch Solel, Solel, Baruch · 1 citation
Mathematics · #46B99 #46L07 #46L08 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46B99 #msc:46L07 #msc:46L08

paper · pdf · doi:10.48550/arxiv.math/0104188

41 pages, Latex, To appear in the Transactions of AMS

arxiv created 2001/04/19 · openalex publication_date 2001/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module actions. Every such isometry can be extended to an isometry of the C* linking algebras.

Cited by

• C*-submodule preserving module mappings on Hilbert C*-modules

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