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.

Keywords: $H^*$-algebra, Hilbert $H^*$-module, bounded operator

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