Twisting Operator Spaces
Operator Algebras
2017-04-26 v1 Functional Analysis
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 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.
Cite
@article{arxiv.1704.07760,
title = {Twisting Operator Spaces},
author = {Willian Hans Goes Corrêa},
journal= {arXiv preprint arXiv:1704.07760},
year = {2017}
}
Comments
37 pages