A NOTE ON EXTENSIONS OF HILBERT C-MODULES AND THEIR MORPHISMS

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 rst 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 dened in [5]. 1