#### 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.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.41.2.13

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