Complex Strict Convexity of Certain Banach Spaces.
Composition results for strongly summing and dominated multilinear operators
In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.
Compound invariants and embeddings of Cartesian products
New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.
Containing l1 or c0 and best approximation.
The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.
Continuous and generalized solutions of singular partial differential equations.
Continuous restrictions of linear functionals
Copies of C0 in Certain Vector-Valued Function Banach Spaces.
Copies of and in Musielak-Orlicz sequence spaces
Criteria in order that a Musielak-Orlicz sequence space contains an isomorphic as well as an isomorphically isometric copy of are given. Moreover, it is proved that if , where are defined on a Banach space, does not satisfy the -condition, then the Musielak-Orlicz sequence space of -valued sequences contains an almost isometric copy of . In the case of it is proved also that if contains an isomorphic copy of , then does not satisfy the -condition. These results extend some...
Copies of lp in tensor products.
The problem of finding complemented copies of lp in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of lp in an n-fold tensor product of lq spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.
Correction to the paper: Support functionals and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm
Cotype for p-Banach spaces
Cotype of operators from C(K).