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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Twisting operator spaces


Author: Willian Hans Goes Corrêa
Journal: Trans. Amer. Math. Soc. 370 (2018), 8921-8957
MSC (2010): Primary 47L25; Secondary 46M18, 47L30
DOI: https://doi.org/10.1090/tran/7461
Published electronically: August 8, 2018
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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.


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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

DOI: https://doi.org/10.1090/tran/7461
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
Article copyright: © Copyright 2018 American Mathematical Society

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