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$R$ -Boundedness versus $\gamma$ -boundedness

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Apr 2016 Germany, Netherlands Publisher:International Press of BostonJournal:Arkiv för Matematik, volume 54, pages 125-145 (issn: 0004-2080,

Authors: Kwapien, Stanislaw; Veraar, Mark; Weis, Lutz;

doi: 10.1007/s11512-015-0223-1

arXiv: http://arxiv.org/abs/1404.7328

$R$ -Boundedness versus $\gamma$ -boundedness

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Abstract

It is well-known that in Banach spaces with finite cotype, the $R$-bounded and $\gamma$-bounded families of operators coincide. If in addition $X$ is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that $R$-boundedness implies $\gamma$-boundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that $R$-boundedness is stable under taking adjoints if and only if the underlying space is $K$-convex.

Comment: Accepted for publication in Arkiv f\"or Matematik

Countries

Germany, Netherlands

Related Organizations

Polish Academy of Sciences
Poland
Delft University of Technology
Netherlands
Karlsruhe Institute of Technology
Germany
University of Warsaw
Poland
Institute of Mathematics
Poland

Keywords

ddc:510, Mathematics - Functional Analysis, 47B99 (Primary), 46B09, 46B07, 47B10 (Secondary), Mathematics, info:eu-repo/classification/ddc/510, Mathematics - Probability, 510

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$R$-boundedness versus $��$-boundedness
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