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