Schauder decompositions in Banach spaces

Schauder decompositions in locally convex spaces

L−maximal Regularity on Banach Spaces with a Schauder Basis

We investigate the problem of L p-maximal regularity on Ba-nach spaces having a Schauder basis. Our results improve those of a recent paper.

Schauder Decompositions and Completeness

00 It x = S QnIf» m addition, the projections Pn = £ Q,are equicontinuous, then n = 1 « = 1 (£n)^°=1 is said to be an equi-Schauder decomposition of E. It is obvious that a Schauder basis is equivalent to a Schauder decomposition in which each subspace is one-dimensional, and that it is equi-Schauder if and only if the corresponding decomposition is equi-Schauder. For more information on Schaud...

Skipped Blocking and Other Decompositions in Banach Spaces

Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces (Xn) can be blocked to be a skipped blocking decompositon (SBD). The condition is order independent, so permutations of conditional basis, for example can be so blocked. This condition is implied if (Xn) is shrinking, or (Xn) is a permutation of a FDD, or if X is reflexive and (Xn) is separating. A...

Duality, Reflexivity and Atomic Decompositions in Banach Spaces

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking” and “boundedly complete” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. ...