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HILBERT $C*$-MODULE VALUED FUNCTIONS AND MULTIPLICATION OPERATORS
Keywords:
Hilbert C*-module, compact operator, multiplication operator, multipliersDOI:
https://doi.org/10.17654/0972087126028Abstract
Let M be a Hilbert module over a C*-algebra A and let X be a locally compact space with a Radon measure. In this article, we introduce an A-valued product for M-valued functions on X which arises from the A-valued inner product of M. We associate a multiplication operator with the aforementioned product and investigate some of their major properties. Notably, we prove that every multiplication operator can be approximated by a net of elementary A-compact operators. Furthermore, assuming that X is a locally compact group, we provide a necessary and sufficient condition under which the multiplication operators are multipliers for integrable functions.
Received: September 1, 2025
Accepted: October 1, 2025
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