# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsFunctional Analysismathscidoc:1701.03034

Arkiv for Matematik, 54, (1), 125-145, 2014.11
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.
@inproceedings{stanislaw2014$r$,
title={ $R$ -Boundedness versus $\gamma$ -boundedness},
author={Stanislaw Kwapień, Mark Veraar, and Lutz Weis},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203642239366096},
booktitle={Arkiv for Matematik},
volume={54},
number={1},
pages={125-145},
year={2014},
}
Stanislaw Kwapień, Mark Veraar, and Lutz Weis. $R$ -Boundedness versus $\gamma$ -boundedness. 2014. Vol. 54. In Arkiv for Matematik. pp.125-145. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203642239366096.