An Indecomposable and unconditionally saturated Banach space

Spiros A. Argyros; A. Manoussakis

An Indecomposable and unconditionally saturated Banach space

Functional Analysis 2016-09-22 v1

Authors: Spiros A. Argyros , A. Manoussakis

Abstract

We construct an indecomposable reflexive Banach space $X_{ius}$ such that every infinite dimensional closed subspace contains an unconditional basic sequence. We also show that every operator $T\in \mathcal{B}(X_{ius})$ is of the form $\lambda I+S$ with $S$ a strictly singular operator.

Keywords

operator theory on banach spaces banach spaces banach space properties

Cite

@article{arxiv.1609.06509,
  title  = {An Indecomposable and unconditionally saturated Banach space},
  author = {Spiros A. Argyros and A. Manoussakis},
  journal= {arXiv preprint arXiv:1609.06509},
  year   = {2016}
}

Comments

25 pages, Dedicated to Professor Aleksander Pe{\l}czy\'nski on the occasion of his 70th birthday

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