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Of operator algebras and operator spaces

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If you have a question about this talk, please contact Richard Garner.

One of the recent advances in Functional Analysis has been the introduction of the notion of an (abstract) operator space. This can be seen as a refinement of the notion of a Banach space which (among other things) solves the problem that not every Banach algebra is an operator algebra. Which theorems about Banach spaces generalise to operator spaces? This question would be easier to answer if one could prove Pestov’s Conjecture: that there exists a Grothendieck topos whose internal Banach spaces are equivalent to operator spaces. I will report on progress towards proving Pestov’s conjecture.

This talk is part of the Category Theory Seminar series.

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