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We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth.[...]texto impreso
We relate the moduli of asymptotic uniform smoothness and convexity of a Banach space with the existence of upper and lower l(p)-estimates of sequences in the space. To this end, we introduce two properties which are related to the (m(p))-proper[...]texto impreso
We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the r[...]texto impreso
In this paper we study the connections between moduli of asymptotic convexity and smoothness of a Banach space, and the existence of high order differentiable bump functions or equivalent norms on the space. The existence of a high order uniform[...]texto impreso
We investigate the best order of smoothness of L-p(L-q). We prove in particular that there exists a C-infinity-smooth bump function on L-p(L-q) if and only if p and q are even integers and p is a multiple of q.texto impreso
An upper bound for the order of smoothness of bump functions in Banach spaces without copy of c(0) is found in terms of lower and upper estimates of their sequences. It is also shown that every C-infinity-smooth Banach space with symmetric basis[...]
