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arXiv · 1404.7328

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

Stanislaw Kwapień·Mark Veraar·Lutz Weis
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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.

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Stanislaw Kwapień, Mark Veraar, Lutz Weis. 2014-04-29. $R$-boundedness versus $\gamma$-boundedness. https://doi.org/10.1007/s11512-015-0223-1

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