Glasnik Matematicki, Vol. 38, No.2 (2003), 341-357.


Damir Bakić and Boris Guljaš

Department of Mathematics, University of Zagreb, P.O. Box 335, 10002 Zagreb, Croatia

Abstract.   We describe the pullback construction in the category of Hilbert C*-modules (with a suitable class of morphisms) in terms of pullbacks of underlying C*-algebras. In the second section the Busby invariant for extensions of Hilbert C*-modules is introduced and it is proved that each extension is uniquely determined, up to isomorphism, by the corresponding Busby map. The induced extensions of the underlying C*-algebras as well as of the corresponding linking algebras are also discussed. The paper ends with a Hilbert C*-module version of a familiar result which states that a C*-algebra is projective if and only if it is corona projective.

2000 Mathematics Subject Classification.   46C50, 46L08.

Key words and phrases.   Hilbert C*-module, adjointable operator, extension, multiplier algebra.

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