On O^*-representability and C^*-representability of *-algebras

2007/09/24 by Stanislav Popovych, Popovych, Stanislav
Mathematics · #06F25 #46L05 #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0709.3741

openalex publication_date 2007/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given. These conditions are generalization of the unshrinkability of monomial *-algebras introduced by C. Lance and P. Tapper. The applications to *-doubles, monomial *-algebras and several other classes of *-algebras are presented.

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