• Corpus ID: 5824881

Factorization of weakly continuous holomorphic mappings

@article{Gonzlez1996FactorizationOW,
  title={Factorization of weakly continuous holomorphic mappings},
  author={Manuel Gonz{\'a}lez and Joaqu{\'i}n M. Guti{\'e}rrez},
  journal={Studia Mathematica},
  year={1996},
  volume={118},
  pages={117-133}
}
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is… 
Compact factorization of differentiable mappings
. Results on factorization (through linear operators) of polynomials and holomorphic mappings between Banach spaces have been obtained in recent years by several authors. In the present paper, we
Schauder type theorems for differentiable and holomorphic mappings
AbstractDenoting byCwup(E) the algebra of allCp-real-valued functions on the real Banach spaceE such that the functions and the derivatives are weakly uniformly continuous on bounded subsets, it is
Some applications of uniformly $ p $-convergent sets
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship
INJECTIVE FACTORIZATION OF HOLOMORPHIC MAPPINGS
We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = g ◦ T , where g is another holomorphic mapping and T is an operator belonging to a closed
Factorization Theorem through a Dunford-Pettis $p$-convergent operator
In this article, we introduce the notion of $p$-$(DPL)$ sets.\ Also, a factorization result for differentiable mappings through Dunford-Pettis $p$-convergent operators is investigated.\ Namely, if $
The Tensor Product Representation of Polynomials of Weak Type in a DF-Space
Let and be locally convex spaces over and let be the space of all continuous -homogeneous polynomials from to . We denote by the -fold symmetric tensor product space of endowed with the projective
The polynomial property (V)
Abstract. Given Banach spaces E and F, we denote by ${\cal P}(^k\! E,F)$ the space of all k-homogeneous (continuous) polynomials from E into F, and by ${\cal P}_{\mathop {\rm wb}\nolimits }(^k\!
Surjective factorization of holomorphic mappings
We characterize the holomorphic mappings $f$ between complex Banach spaces that may be written in the form $f=T\circ g$, where $g$ is another holomorphic mapping and $T$ belongs to a closed
Weakly $p$-sequentially continuous differentiable mappings
In this paper, we introduce the notions uniformly p-convergent sets and weakly p-sequentially continuous differentiable mappings. Then we obtain a sufficient condition for those Banach spaces which
...
1
2
...

References

SHOWING 1-10 OF 30 REFERENCES
Weakly Continuous Mappings on Banach Spaces with the Dunford-Pettis Property
Abstract The Dunford-Pettis weak (dw) topology on a Banach space is introduced as the finest topology that coincides with the weak topology on Dunford-Pettis sets. We characterize a wide class of
The compact weak topology on a Banach space
Throughout [this paper], E and F will denote Banach spaces. The bounded weak topology on a Banach space E, noted bw(E) or simply bw, is defined as the finest topology that agrees with the weak
EXTENSION OF HOLOMORPHIC MAPPINGS FROM E TO E
Assuming that E is a distinguished locally convex space and F is a complete locally convex space, we prove that there exists an open subset V of E" that contains E and such that every holomorphic
Compactly determined locally convex topologies
If E is a Hausdorff locally convex space, there is a finest locally convex topology having the same compact subsets as the original one. The new space is denoted by f E (notice that E and fE have the
Homomorphisms between algebras of differentiable functions in infinite dimensions.
Let E and F be two real Banach spaces. For n = 0, 1, ...,1, let Cnw ub(E; F) be the space of n-times continuously differentiable functions f: E ! F such that, for each integer j _ n and each x 2 E,
Weakly continuous mappings on Banach spaces
Estimates by polynomials
Consider the following possible properties which a Banach space X may have: (P): If (xi) and (yj) are bounded sequences in X such that for all n ≥ 1 and for every continuous n-homogeneous polynomial
...
1
2
3
...