Print Email Facebook Twitter R-Boundedness versus γ-boundedness Title R-Boundedness versus γ-boundedness Author Kwapień, Stanislaw (University of Warsaw) Veraar, M.C. (TU Delft Analysis) Weis, Lutz (Karlsruhe Institut für Technologie) Date 2016 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. To reference this document use: http://resolver.tudelft.nl/uuid:ee794af2-aea0-41ae-ac87-5d4985a95239 DOI https://doi.org/10.1007/s11512-015-0223-1 ISSN 0004-2080 Source Arkiv foer Matematik, 54 (1), 125-145 Part of collection Institutional Repository Document type journal article Rights © 2016 Stanislaw Kwapień, M.C. Veraar, Lutz Weis Files PDF 1971719.pdf 1.14 MB Close viewer /islandora/object/uuid:ee794af2-aea0-41ae-ac87-5d4985a95239/datastream/OBJ/view