engleski

Operators on Hilbert H*-modules

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 describe bounded ${;\cal E};$-linear operators by lifting the appropriate results from Hilbert space theory. In particular, generalized compact ${;\cal E};$-linear operators are characterized.

H*-algebra ; H*-module ; bounded operator

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