Isomorphic Schauder decompositions in certain 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...

Isomorphic universality and the number of pairwise non-isomorphic models in the class of Banach spaces

1 We develop the framework of natural spaces to study isomorphic embeddings of Banach spaces. We then use it to show that a sufficient failure of the generalized continuum hypothesis implies that the universality number of Banach spaces of a given density under a certain kind of positive embeddings (very positive embeddings), is high. An example of a very positive embedding is a positive onto e...

Linear Functionals on Certain Banach Spaces