Glasnik Matematicki, Vol. 41, No.2 (2006), 309-315.

MORPHISMS OUT OF A SPLIT EXTENSION OF A HILBERT C*-MODULE

Biserka Kolarec

Department of Informatics and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska cesta 25, 10000 Zagreb, Croatia
e-mail: bkudelic@agr.hr


Abstract.   Let us have a split extension W of a Hilbert C*-module V by a Hilbert C*-module Z. Like in the case of C*-algebras (well known theorem of T. A. Loring), every morphism out of W, more precisely from W to an arbitrary Hilbert C*-module U, can be described as a pair of morphisms from V and Z, respectively, into U that satisfies certain conditions. It turns out that besides the generalization of the Loring's condition, an additional condition has to be posed.

2000 Mathematics Subject Classification.   46C50, 46L08.

Key words and phrases.   Hilbert C*-module, ideal submodule, (split) extension, morphism.


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DOI: 10.3336/gm.41.2.13


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