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Title

A STRONG VERSION OF THE BIRKHOFF–JAMES ORTHOGONALITY IN HILBERT C*-MODULES

Pages

 Start Page 109 | End Page 120

Keywords

HILBERT C*-MODULE 

Abstract

 In this paper we introduce a strong version of the BIRKHOFF–JAMES ORTHOGONALITY in Hilbert C*-modules. More precisely, we consider elements x and y of a Hilbert C*-module V over a C*-algebra A which satisfy ||x||£||x+ya|| for all a Î A. We show that this relation can be described as the BIRKHOFF–JAMES ORTHOGONALITY of appropriate elements of V, and characterized in terms of STATEs acting on the underlying C*-algebra A. Some analogous relations of this type are considered as well.

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