Twisting operator spaces

Corrêa, Willian Hans

doi:10.1090/tran/7461

Twisting operator spaces
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by Willian Hans Goes Corrêa PDF

Trans. Amer. Math. Soc. 370 (2018), 8921-8957 Request permission

Abstract:

In this work we study the following three-space problem for operator spaces: if $X$ is an operator space with base space isomorphic to a Hilbert space and $X$ contains a completely isomorphic copy of the operator Hilbert space $OH$ with the respective quotient also completely isomorphic to $OH$, must $X$ be completely isomorphic to $OH$? This problem leads us to the study of short exact sequences of operator spaces, more specifically those induced by complex interpolation and their splitting. We show that the answer to the three-space problem is negative, giving two different solutions.

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