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On the complexity of some classes of Banach spaces and non-universality

Bruno M. Braga (2014)

Czechoslovak Mathematical Journal

These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded operators,...

On the Composition Operator in AC[a,b].

Nelson Merentes (1991)

Collectanea Mathematica

Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.

On the continuity of Bessel potentials in Orlicz spaces.

N. Aïssaoui (1996)

Collectanea Mathematica

It is shown that Bessel capacities in reflexive Orlicz spaces are non increasing under orthogonal projection of sets. This is used to get a continuity of potentials on some subspaces. The obtained results generalize those of Meyers and Reshetnyak in the case of Lebesgue classes.

On the control measures of vector measures.

Baltasar Rodríguez-Salinas (2003)

RACSAM

Si Σ es una σ-álgebra y X un espacio localmente convexo se estudian las condiciones para las cuales una medida vectorial σ-aditiva γ : Σ → χ tenga una medida de control μ. Si Σ es la σ-álgebra de Borel de un espacio métrico, se obtienen condiciones necesarias y suficientes usando la τ aditividad de γ. También se dan estos resultados para las polimedidas.

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