Twisting operator spaces
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- by Willian Hans Goes Corrêa PDF
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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.References
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Additional Information
- Willian Hans Goes Corrêa
- Affiliation: Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo SP, Brazil
- Email: willhans@ime.usp.br
- Received by editor(s): April 27, 2017
- Received by editor(s) in revised form: October 30, 2017
- Published electronically: August 8, 2018
- Additional Notes: This work was partially supported by CAPES, Coordination of Improvement of Higher Level Personnel - Brazil, grant 1328372, and by CNPq, National Council for Scientific and Technological Development - Brazil, grant 140413/2016-2
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 8921-8957
- MSC (2010): Primary 47L25; Secondary 46M18, 47L30
- DOI: https://doi.org/10.1090/tran/7461
- MathSciNet review: 3864400