On stable maps of operator algebras

2018/12/11 by George Eleftherakis, Eleftherakis, G. K. · 1 citation
Mathematics · #16D90 (secondary) #46L05 #47L05 #47L25 #47L30 (primary) #47L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1812.04338

openalex publication_date 2018/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a strong Morita-type equivalence ∼ _σΔ for operator algebras. We prove that A∼ _σΔB if and only if A and B are stably isomorphic. We also define a relation ⊂ _σΔ for operator algebras. We prove that if A and B are C^*-algebras, then A⊂ _σΔ B if and only if there exists an onto *-homomorphism θ:B⊗ \mathcal K → A⊗ \mathcal K, where \mathcal K is the set of compact operators acting on an infinite dimensional separable Hilbert space. Furthermore, we prove that if A and B are C^*-algebras such that A⊂ _σΔ B and B⊂ _σΔ A , then there exist projections r, r in the centers of A^** and B^**, respectively, such that Ar∼ _σΔB r and A (id_A^**-r) ∼ _σΔB(id_B^**- r).

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• Morita equivalence and stable isomorphism via unitary operators

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