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Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz

N. MerentesJ. L. Sánchez Hernández — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space R V φ ( [ a , b ] ; K ) into R W φ ( [ a , b ] ; C C ( Y ) ) (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t)) = A(t)u(t)...

Some remarks on the algebra of functions of two variables with bounded total Φ -variation in Schramm sense

Tomás EreúNelson MerentesJosé L. Sánchez — 2010

Commentationes Mathematicae

This paper is devoted to discuss some generalizations of the bounded total Φ -variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total Φ -variation in Schramm sense has the structure of a Banach algebra.

Embedding c 0 in bvca ( Σ , X )

Juan Carlos FerrandoL. M. Sánchez Ruiz — 2007

Czechoslovak Mathematical Journal

If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

Pták homomorphism theorem revisited

J. R. FerrerM. López PellicerL. M. Sánchez Ruiz — 2000

Czechoslovak Mathematical Journal

Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.

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