LINEAR ORTHOGONALITY PRESERVERS OF HILBERT C*-MODULES
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AbstractWe show in this paper that the module structure and the orthogonality structure of a Hilbert C*-module determine its inner product structure. Let A be a C*-algebra, and E and F be Hilbert A-modules. Assume Phi : E -> F is an A-module map satisfying (A) = 0 whenever < x,y >(A) = 0. Then Phi is automatically bounded. In case Phi is bijective, E is isomorphic to F. More precisely, let J(E) be the closed two-sided ideal of A generated by the set {< x,y >(A) : x,y is an element of E}. We show that there exists a unique central positive multiplier u is an element of M(J(E)) such that (A) = u < x,y >(A) (x,y is an element of E). As a consequence, the induced map Phi(0) : E -> (Phi) over bar((E) over bar) is adjointable, and (Eu-1/2) over bar is isomorphic to (Phi) over bar((E) over bar) as Hilbert A-modules.
All Author(s) ListLeung CW, Ng CK, Wong NC
Journal nameJOURNAL OF OPERATOR THEORY
Detailed descriptionTo ORKTS: This paper accepted for publication in the Journal of Operator Theory
Year2014
Month3
Day1
Volume Number71
Issue Number2
PublisherTHETA FOUNDATION
Pages571 - 584
ISSN0379-4024
LanguagesEnglish-United Kingdom
Keywordsauto continuity; Hilbert C*-modules; Orthogonality preservers; Uhl horn theorem
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-07-04 at 00:56