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A theorem of the Hahn-Banach type and its applications

Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor (1992)

Annales Polonici Mathematici

Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.

A uniform boundedness principle of Pták

Charles W. Swartz (1993)

Commentationes Mathematicae Universitatis Carolinae

The Antosik-Mikusinski Matrix Theorem is used to give an extension of a uniform boundedness principle due to V. Pták to certain metric linear spaces. An application to bilinear operators is given.

A useful algebra for functional calculus

Mohammed Hemdaoui (2019)

Mathematica Bohemica

We show that some unital complex commutative LF-algebra of 𝒞 ( ) -tempered functions on + (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

About some parameters of normed linear spaces

Emanuele Casini (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prendono in considerazione particolari costanti relative alla struttura della sfera unitaria di uno spazio di Banach. Se ne studiano alcune generali proprietà, con particolare riferimento alle relazioni con il modulo di convessità dello spazio. Se ne fornisce inoltre una esatta valutazione negli spazi l p .

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