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Stably isomorphic dual operator algebras

Authors:	G K Eleftherakis V I Paulsen

Institution:	(1) Department of Mathematics, University of Athens, Athens, Greece;(2) Department of Mathematics, University of Houston, Houston, TX 77204, USA

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 ${\beta(B) = \mathcal{M}\alpha(A)\mathcal{M}^]^{-w^*}.}$ This project is cofunded by European Social Fund and National Resources—(EPEAEK II) “Pyhtagoras II” grant No. 70/3/7997.

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