Abstract
We introduce the notion of \(\Delta \) and \(\sigma \,\Delta -\) pairs for operator algebras and characterise \(\Delta -\) pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of \(\Delta \)-Morita equivalent operator spaces and prove a similar theorem about their algebraic extensions. We prove that \(\sigma \Delta \)-Morita equivalent operator spaces are stably isomorphic and vice versa. Finally, we study unital operator spaces, emphasising their left (resp. right) multiplier algebras, and prove theorems that refer to \(\Delta \)-Morita equivalence of their algebraic extensions.
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Eleftherakis, G.K., Papapetros, E. A Morita Characterisation for Algebras and Spaces of Operators on Hilbert Spaces. Integr. Equ. Oper. Theory 92, 51 (2020). https://doi.org/10.1007/s00020-020-02611-7
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DOI: https://doi.org/10.1007/s00020-020-02611-7