On the Definition of C (a Summary of a Talk given at Pssl#85 in Nice)
نویسنده
چکیده
One of the recent advances in Functional Analysis has been the introduction of the notion of an (abstract) operator space. Proponents of this theory have, since its inception, maintained that it provides a much more solid " foundations " for Operator Algebra than the more traditional theory of Banach spaces. In this paper, we show that there exists a (non-trivial) involutive monoidal structure on the category of operator spaces and linear complete contractions. Every C *-algebra gives rise to an involutive monoid in this involutive monoidal category, but (unfortunately) not vice versa.
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