LINEAR ORTHOGONALITY PRESERVERS OF HILBERT BUNDLES
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AbstractA C-linear map theta (not necessarily bounded) between two Hilbert C*-modules is said to be 'orthogonality preserving' if = 0 whenever < x, y > = 0. We prove that if theta is an orthogonality preserving map from a full Hilbert C(0)(Omega)-module E into another Hilbert C(0)(Omega)-module F that satisfies a weaker notion of C(0)(Omega)-linearity (called localness'), then theta is bounded and there exists phi is an element of C(b)(Omega)(+) such that = phi < x, y > for all x, y is an element of E.
All Author(s) ListLeung CW, Ng CK, Wong NC
Journal nameJournal of the Australian Mathematical Society
Year2010
Month10
Day1
Volume Number89
Issue Number2
PublisherCambridge University Press (CUP): STM Journals - No Cambridge Open
Pages245 - 254
ISSN1446-7887
LanguagesEnglish-United Kingdom
Keywordsautomatic continuity; Hilbert bundles; Hilbert C*-modules; local maps; module homomorphisms; orthogonality preserving maps
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-24-10 at 01:12