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Twisted Hilbert spaces

Published online by Cambridge University Press:  17 April 2009

Félix Cabello Sánchez
Félix Cabello Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avda de Elvas s/n, 06071 Badajoz, Spain e-mail: fcabello@unex.es
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Abstract

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A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y such that the corresponding quotient is isomorphic to Z. A twisted Hilbert space is a twisted sum of Hilbert spaces. We prove the following tongue-twister: there exists a twisted sum of two subspaces of a twisted Hilbert space that is not isomorphic to a subspace of a twisted Hilbert space. In other words, being a subspace of a twisted Hilbert space is not a three-space property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 177 - 180
Copyright
Copyright © Australian Mathematical Society 1999

References

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