Geodesic
Quotient Hereditarily Indecomposable Banach Spaces
Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 566-584

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1999-026-4
Mots-clés : 46B20, 47B99 
Ferenczi, V. Quotient Hereditarily Indecomposable Banach Spaces. Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 566-584. doi: 10.4153/CJM-1999-026-4
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