Journal of Operator Theory

Volume 46, Issue 1, Summer 2001 pp. 123-137.

Operators on Hilbert

$H^*$ -modules

Authors: Damir Bakic (1), and Boris Guljas (2)
Author institution: (1) Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia
(2) Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia

Summary: Let

$W$ be a Hilbert

$H^*$ -module over an

$H^*$ -algebra

${\cal E}$ . We show that all bounded

${\cal E}$ -linear operators on

$W$ are reduced by a suitable Hilbert space contained in

$W$ . This enables us to de scribe bounded

${\cal E}$ -linear operators by lifting the appropriate results fr om Hilbert space theory. In particular, generalized compact

${\cal E}$ -linear operators are characterized.

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