Hilbert modules over locally C*-algebras
Yu. I. Zhuraev, F. Sharipov (Samarkand State Univ.)

TL;DR
This paper explores Hilbert modules over locally C*-algebras, proving that their adjointable endomorphisms form a locally C*-algebra, thus extending the understanding of module structures in this context.
Contribution
It provides a detailed proof that the set of adjointable endomorphisms of Hilbert modules over locally C*-algebras is itself a locally C*-algebra, clarifying foundational properties.
Findings
The set of adjointable endomorphisms forms a locally C*-algebra.
Detailed proof of the main structural result.
Enhanced understanding of Hilbert modules over locally C*-algebras.
Abstract
In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms of such modules is itself a locally C*-algebra.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory
