Abstract
We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Δ-equivalent (Eleftherakis in J Pure Appl Algebra, ArXiv:math. OA/0607489v4, 2007), if and only if they have completely isometric normal representations α,β on Hilbert spaces H, K respectively and there exists a ternary ring of operators \({\mathcal{M} \subset B(H, K)}\) such that \({\alpha (A) = [\mathcal{M}^* \beta(B)\mathcal{M}]^{-w^*}}\) and \({\beta(B) = [\mathcal{M}\alpha(A)\mathcal{M}^*]^{-w^*}.}\)
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This project is cofunded by European Social Fund and National Resources—(EPEAEK II) “Pyhtagoras II” grant No. 70/3/7997.
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Eleftherakis, G.K., Paulsen, V.I. Stably isomorphic dual operator algebras. Math. Ann. 341, 99–112 (2008). https://doi.org/10.1007/s00208-007-0184-1
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DOI: https://doi.org/10.1007/s00208-007-0184-1