Abstract:An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some $l_p$-type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.
Keywords: Banach space, nearly uniform smoothness, finite dimensional decomposition, Banach-Saks property, fixed point property
AMS Subject Classification: 46B20, 47H10