2014/04/14 by George Eleftherakis, Eleftherakis, G. K. · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1404.3746
openalex publication_date 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a Morita type equivalence: two operator algebras A and B are called strongly Δ-equivalent if they have completely isometric representations α and β respectively and there exists a ternary ring of operators M such that α(A) (resp. β(B)) is equal to the norm closure of the linear span of the set M^*β(B)M, (resp. Mα(A)M^*). We study the properties of this equivalence. We prove that if two operator algebras A and B, possessing countable approximate identities, are strongly Δ-equivalent, then the operator algebras A⊗ \cl K and B⊗ \cl K are isomorphic. Here \cl K is the set of compact operators on an infinite dimensional separable Hilbert space and ⊗ is the spatial tensor product. Conversely, if A⊗ \cl K and B⊗ \cl K are isomorphic and A, B possess contractive approximate identities then A and B are strongly Δ-equivalent.