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On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

Enrique A. Sánchez-Pérez (1996)

Collectanea Mathematica

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...

On the structure of the set of higher order spreading models

Bünyamin Sarı, Konstantinos Tyros (2014)

Studia Mathematica

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 S M ξ w ( X ) 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 S M ξ w ( X ) contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if S M ξ w ( X ) is uncountable, then it contains an antichain of size...

On the structure of universal differentiability sets

Michael Dymond (2017)

Commentationes Mathematicae Universitatis Carolinae

A subset of d is called a universal differentiability set if it contains a point of differentiability of every Lipschitz function f : d . 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.

On the support of Fourier transform of weighted distributions

Martha Guzmán-Partida (2010)

Commentationes Mathematicae Universitatis Carolinae

We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region x 1 0 and x 2 0 .

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