BibTeX
@MISC{Kashyap08amorita,
author = {Upasana Kashyap},
title = {A MORITA THEOREM FOR DUAL OPERATOR ALGEBRAS},
year = {2008}
}
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Abstract
We prove that two dual operator algebras are weak ∗ Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak ∗-continuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case, we characterize such functors as the module normal Haagerup tensor product with an appropriate weak ∗ Morita equivalence bimodule. We also develop the theory of the W ∗-dilation, which connects the non-selfadjoint dual operator algebra with the W ∗-algebraic framework. In the case of weak ∗ Morita equivalence, this W ∗-dilation is a W ∗-module over a von Neumann algebra generated by the non-selfadjoint dual operator algebra. The theory of the W ∗-dilation is a key part of the proof of our main theorem.
Keyphrases
morita theorem dual operator algebra non-selfadjoint dual operator algebra von neumann algebra operator algebra case contractive functors module normal haagerup tensor product dual operator module algebraic framework appropriate morphism space dual operator algebra weak morita equivalent weak morita equivalence appropriate weak morita equivalence bimodule equivalent category key part main theorem
