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On super-weakly compact sets and uniformly convexifiable sets

Lixin Cheng, Qingjin Cheng, Bo Wang, Wen Zhang (2010)

Studia Mathematica

This paper mainly concerns the topological nature of uniformly convexifiable sets in general Banach spaces: A sufficient and necessary condition for a bounded closed convex set C of a Banach space X to be uniformly convexifiable (i.e. there exists an equivalent norm on X which is uniformly convex on C) is that the set C is super-weakly compact, which is defined using a generalization of finite representability. The proofs use appropriate versions of classical theorems, such as James' finite tree...

On supportless absorbing convex subsets in normed spaces

V. Fonf (1993)

Studia Mathematica

It is proved that a separable normed space contains a closed bounded convex symmetric absorbing supportless subset if and only if this space may be covered (in its completion) by the range of a nonisomorphic operator.

On suprabarrelledness of c0 (Ω, X).

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

Si Ω­ es un conjunto no vacío y X es un espacio normado real o complejo, se tiene que, con la norma supremo, el espacio c0 (Ω, X) formado por las funciones f : Ω­ → X tales que para cada ε > 0 el conjunto {ω ∈ Ω­ : || f(ω) || > ε} es finito es supratonelado si y sólo si X es supratonelado.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra ℝ ¯ of generalized real numbers. It is worth mentioning that the algebra ℝ ¯ is not a field.

On Tauberian and co-Tauberian operators.

Sudipta Dutta, Vladimir P. Fonf (2006)

Extracta Mathematicae

We show that a Banach space X has an infinite dimensional reflexive subspace (quotient) if and only if there exist a Banach space Z and a non-isomorphic one-to-one (dense range) Tauberian (co-Tauberian) operator form X to Z (Z to X). We also give necessary and sufficient condition for the existence of a Tauberian operator from a separable Banach space to c0 which in turn generalizes a result of Johnson and Rosenthal. Another application of our result shows that if X** is separable, then there exists...

On tempered convolution operators

Saleh Abdullah (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that if S is a convolution operator in S ' , and S * S ' = S ' , then the zeros of the Fourier transform of S are of bounded order. Then we discuss relations between the topologies of the space O c ' of convolution operators on S ' . Finally, we give sufficient conditions for convergence in the space of convolution operators in S ' and in its dual.

On the A -integrability of singular integral transforms

Shobha Madan (1984)

Annales de l'institut Fourier

In this article we study the weak type Hardy space of harmonic functions in the upper half plane R + n + 1 and we prove the A -integrability of singular integral transforms defined by Calderón-Zygmund kernels. This generalizes the corresponding result for Riesz transforms proved by Alexandrov.

Currently displaying 1021 – 1040 of 1948