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

### EXTENSIONS OF HILBERT
C^{*}-MODULES II

### Damir Bakić and Boris Guljaš

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

*e-mail:* `bakic@math.hr`

*e-mail:* `guljas@math.hr`

**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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