On quantales that classify C*-algebras ∗
@article{Kruml2004OnQT,
title={On quantales that classify C*-algebras ∗},
author={David Kruml and Pedro Resende},
journal={Cahiers de Topologie et G{\'e}om{\'e}trie Diff{\'e}rentielle Cat{\'e}goriques},
year={2004},
volume={45},
pages={287-296}
}The functor Max of Mulvey assigns to each unital C*-algebra A the unital involutive quantale Max A of closed linear subspaces of A, and it has been remarked that it classifies unital C*-algebras up to ∗-isomorphism. In this paper we provide a proof of this and of the stronger fact that for every isomorphism u : Max A → Max B of unital involutive quantales there is a ∗-isomorphism b : A → B such that Max b u coincides with u when restricted to the left-sided elements of Max A. But we also show…
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