R-Boundedness versus γ-boundedness

Journal article (2016)

Authors

Stanislaw Kwapień University of Warsaw
M.C. Veraar Analysis - EEMCS
L Weis Karlsruhe Institut für Technologie
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2016 Stanislaw Kwapień, M.C. Veraar, Lutz Weis
DOI: https://doi.org/10.1007/s11512-015-0223-1
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Published Date

2016

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

It is well-known that in Banach spaces with finite cotype, the R-bounded and γ-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 γ-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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