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On inverses of δ -convex mappings

Jakub Duda (2001)

Commentationes Mathematicae Universitatis Carolinae

In the first part of this paper, we prove that in a sense the class of bi-Lipschitz δ -convex mappings, whose inverses are locally δ -convex, is stable under finite-dimensional δ -convex perturbations. In the second part, we construct two δ -convex mappings from ℓ 1 onto ℓ 1 , which are both bi-Lipschitz and their inverses are nowhere locally δ -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at 0 . These mappings show that for (locally) δ -convex mappings...

On multilinear generalizations of the concept of nuclear operators

Dahmane Achour, Ahlem Alouani (2010)

Colloquium Mathematicae

This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...

On multilinear mappings attaining their norms.

Maria Acosta (1998)

Studia Mathematica

We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.

On multilinear mappings of nuclear type.

Mário C. Matos (1993)

Revista Matemática de la Universidad Complutense de Madrid

The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.

On non-Uniqueness of Complex Geodesies in Convex Bounded Domains

Graziano Gentili (1985)

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

Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di ℂ in un dominio convesso limitato D di uno spazio di Banach complesso E , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di D .

On perturbations of pluriregular sets generated by sequences of polynomial maps

Maciej Klimek (2003)

Annales Polonici Mathematici

It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.

On Pettis integrability

Juan Carlos Ferrando (2003)

Czechoslovak Mathematical Journal

Assuming that ( Ω , Σ , μ ) is a complete probability space and X a Banach space, in this paper we investigate the problem of the X -inheritance of certain copies of c 0 or ℓ ∞ in the linear space of all [classes of] X -valued μ -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.

On Pettis integral and Radon measures

Grzegorz Plebanek (1998)

Fundamenta Mathematicae

Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable....

On Pettis integrals with separable range

Grzegorz Plebanek (1993)

Colloquium Mathematicae

Several techniques have been developed to study Pettis integrability of weakly measurable functions with values in Banach spaces. As shown by M. Talagrand [Ta], it is fruitful to regard a weakly measurable mapping as a pointwise compact set of measurable functions - its Pettis integrability is then a purely measure-theoretic question of an appropriate continuity of a measure. On the other hand, properties of weakly measurable functions can be translated into the language of topological measure theory...

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