Original scientific paper

A note on extensions of Hilbert C*-modules and their morphisms

Franka Miriam Bruckler

Abstract

The aim of this paper is to connect the results of D. Bakic and B. Guljas about C*-extensions of Hilbert C*-modules with results of D. P. Blecher about Hilbert C*-extensions of operator spaces. In the first part, we give conditions on a completely bounded linear operator between Hilbert C*-modules for the possibility of extending the operator to a "corner-preserving" C*-morphism of the corresponding linking-algebras (or, equivalently, for the operator being a Hilbert C*-morphism). The second part provides an order preserving bijection between the sets of C*-extensions of a Hilbert C*-module and its Hilbert C*-extensions, the latter being a generalized version of Blecher's Hilbert C*-extensions of operator spaces.

Keywords

Hilbert C*-module; operator space; extension; multiplier algebra; completely bounded map

Hrčak ID:

1253

URI

https://hrcak.srce.hr/1253

Publication date:

29.11.2004.

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