$R$-boundedness versus $\gamma$-boundedness
Functional Analysis
2015-09-02 v3 Probability
Abstract
It is well-known that in Banach spaces with finite cotype, the -bounded and -bounded families of operators coincide. If in addition is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that -boundedness implies -boundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that -boundedness is stable under taking adjoints if and only if the underlying space is -convex.
Cite
@article{arxiv.1404.7328,
title = {$R$-boundedness versus $\gamma$-boundedness},
author = {Stanislaw Kwapień and Mark Veraar and Lutz Weis},
journal= {arXiv preprint arXiv:1404.7328},
year = {2015}
}
Comments
Accepted for publication in Arkiv f\"or Matematik