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Quotient Hereditarily Indecomposable Banach Spaces

Published online by Cambridge University Press:  20 November 2018

V. Ferenczi
V. Ferenczi*
Affiliation:
Equipe d’Analyse, Université Paris 6, Tour 46-0, Boîte 186, 4, place Jussieu, 75252 PARIS Cedex 05, France email: ferenczi@ccr.jussieu.fr
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Abstract

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A Banach space $X$ is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of $X$ is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space ${{X}_{GM}}$ constructed by W. T. Gowers and B. Maurey in $[\text{GM}]$. Then we provide an example of a reflexive hereditarily indecomposable space $\hat{X}$ whose dual is not hereditarily indecomposable; so $\hat{X}$ is not quotient hereditarily indecomposable. We also show that every operator on ${{\hat{X}}^{*}}$ is a strictly singular perturbation of an homothetic map.

Keywords

46B2047B99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 3 , 01 June 1999 , pp. 566 - 584
Copyright
Copyright © Canadian Mathematical Society 1999

References

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