A class of Banach spaces with few non strictly singular operators

S. A. Argyros; J. Lopez-Abad; S. Todorcevic

A class of Banach spaces with few non strictly singular operators

Functional Analysis 2007-05-23 v2 Logic

Authors: S. A. Argyros , J. Lopez-Abad , S. Todorcevic

Abstract

We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$ .

Keywords

banach spaces reflexive spaces transfinite basis strictly singular operators unconditional basic sequences bounded operators

Cite

@article{arxiv.math/0312522,
  title  = {A class of Banach spaces with few non strictly singular operators},
  author = {S. A. Argyros and J. Lopez-Abad and S. Todorcevic},
  journal= {arXiv preprint arXiv:math/0312522},
  year   = {2007}
}

Comments

52 pages, 1 figure

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