R-Boundedness versus γ-boundedness

Stanislaw Kwapień, MC Veraar, Lutz Weis

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
42 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)125-145
Number of pages21
JournalArkiv foer Matematik
Volume54
Issue number1
DOIs
Publication statusPublished - 2016

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