Relative compactness of orbits and geometry of Banach spaces

Bálint Farkas; Henrik Kreidler

Relative compactness of orbits and geometry of Banach spaces

Functional Analysis 2020-07-03 v2

Authors: Bálint Farkas , Henrik Kreidler

Abstract

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$ , when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$ . In particular, we derive characterizations of separable Banach spaces not containing $\mathrm{c}_0$ and of reflexivity of Banach spaces with a Schauder basis in terms of such compactness results.

Keywords

relative compactness semigroup of operators banach spaces orbits schauder basis reflexivity

Cite

@article{arxiv.2003.11364,
  title  = {Relative compactness of orbits and geometry of Banach spaces},
  author = {Bálint Farkas and Henrik Kreidler},
  journal= {arXiv preprint arXiv:2003.11364},
  year   = {2020}
}

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