On the Structure of Non-Weakly Compact Operators on Banach Lattices.
We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and Matter. As...
We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if is uncountable, then it contains an antichain of size...
A subset of is called a universal differentiability set if it contains a point of differentiability of every Lipschitz function . We show that any universal differentiability set contains a ‘kernel’ in which the points of differentiability of each Lipschitz function are dense. We further prove that no universal differentiability set may be decomposed as a countable union of relatively closed, non-universal differentiability sets.
We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region and .