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

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

Biserka Kolarec

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.

DOI: 10.3336/gm.41.2.13

References:

1. D. Bakic and B. Guljas, Extensions of Hilbert C*-modules, Houston J. of Math. 30 (2004), 537-558.
   MathSciNet

2. D. Bakic and B. Guljas, Extensions of Hilbert C*-modules. II, Glas. Mat. Ser. III 38(58) (2003), 341-357.
   MathSciNet

3. E. C. Lance, Hilbert C*-modules. A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge, 1995.
   MathSciNet

4. T. A. Loring, Lifting Solutions to Perturbing Problems in C*-algebras, American Mathematical Society, Providence, 1997.
   MathSciNet

5. I. Raeburn and D. P. Williams, Morita Equivalence and Continuous-Trace C*-algebras, American Mathematical Society, Providence, 1998.
   MathSciNet

6. N. E. Wegge-Olsen, K-theory and C*-algebras. A Friendly Approach, The Clarendon Press, Oxford University Press, New York, 1993.
   MathSciNet