TY - JOUR
T1 - R-Boundedness versus γ-boundedness
AU - Kwapień, Stanislaw
AU - Veraar, MC
AU - Weis, Lutz
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
UR - http://resolver.tudelft.nl/uuid:ee794af2-aea0-41ae-ac87-5d4985a95239
U2 - 10.1007/s11512-015-0223-1
DO - 10.1007/s11512-015-0223-1
M3 - Article
SN - 0004-2080
VL - 54
SP - 125
EP - 145
JO - Arkiv foer Matematik
JF - Arkiv foer Matematik
IS - 1
ER -