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Small ball properties for Fréchet spaces.

Leonhard Frerick, Alfredo Peris (2003)

RACSAM

We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.

Some characterizations of order weakly compact operator

Belmesnaoui Aqzzouz, Aziz Elbour (2011)

Mathematica Bohemica

We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

Some properties and applications of equicompact sets of operators

E. Serrano, C. Piñeiro, J. M. Delgado (2007)

Studia Mathematica

Let X and Y be Banach spaces. A subset M of (X,Y) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xₙ) in X has a subsequence such that is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion...

Stochastic continuity and approximation

Leon Brown, Bertram Schreiber (1996)

Studia Mathematica

This work is concerned with the study of stochastic processes which are continuous in probability, over various parameter spaces, from the point of view of approximation and extension. A stochastic version of the classical theorem of Mergelyan on polynomial approximation is shown to be valid for subsets of the plane whose boundaries are sets of rational approximation. In a similar vein, one can obtain a version in the context of continuity in probability of the theorem of Arakelyan on the uniform...

Sur la conorme essentielle

Mostafa Mbekhta, Rodolphe Paul (1996)

Studia Mathematica

Pour un opérateur T borné sur un espace de Hilbert dans lui-même, nous montrons que , où γ est la conorme (the reduced minimum modulus) et π(T) est la classe de T dans l’algèbre de Calkin. Nous montrons aussi que ce supremum est atteint. D’autre part, nous montrons que les opérateurs semi-Fredholm caractérisent les points de continuité de l’application T → γ (π(T)).

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