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Mazur spaces.

Wilansky, Albert (1981)

International Journal of Mathematics and Mathematical Sciences

Mazur-like topological linear spaces and their products

Miroslav Hušek (1997)

Commentationes Mathematicae Universitatis Carolinae

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

Mazur-Orlicz equality

Fon-Che Liu (2008)

Studia Mathematica

A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.

Measure of noncompactness of linear operators between spaces of sequences that are ( N ¯ , q ) summable or bounded

Eberhard Malkowsky, V. Rakočević (2001)

Czechoslovak Mathematical Journal

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are ( N ¯ , q ) summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.

Measures of non-compactness in Orlicz modular spaces.

A. G. Aksoy, J.-B. Baillon (1993)

Collectanea Mathematica

In this paper we show that the ball-measure of non-compactness of a norm bounded subset of an Orlicz modular space L-Psi is equal to the limit of its n-widths. We also obtain several inequalities between the measures of non-compactness and the limit of the n-widths for modular bounded subsets of L-Psi which do not have Delta-2-condition. Minimum conditions on Psi to have such results are specified and an example of such a function Psi is provided.

Metrizability of precompact sets: an elementary proof.

J. C. Ferrando, J. Kakol, M. López Pellicer (2005)

RACSAM

Proporcionamos una demostración muy corta de un teorema de Cascales-Orihuela que establece que todo conjunto precompacto de un espacio localmente convexo de la clase G (en el sentido de Cascales-Orihuela) es metrizable.

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