Erratum: Three Conjectures of Combinatorial Topology.
Polynomial characterizations of Banach spaces not containing l.
Many properties of Banach spaces can be given in terms of (linear bounded) operators. It is natural to ask if they can also be formulated in terms of polynomial, holomorphic and continuous mappings. In this note we deal with Banach spaces not containing an isomorphic copy of l, the space of absolutely summable sequences of scalars.
Partial homotopy type of finite two-complexes.
Infragradientes y direcciones de decrecimiento.
Extension and lifting of weakly continuous polynomials
We show that a Banach space X is an ℒ₁-space (respectively, an -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an -space.
Polynomial characterizations of the Dunford-Pettis property.
We introduce and characterize the class P of polynomials between Banach spaces whose restrictions to Dunford-Pettis (DP) sets are weakly continuous. All the weakly compact and the scalar valued polynomials belong to P. We prove that a Banach space E has the Dunford-Pettis (DP) property if and only if every P ∈ P is weakly sequentially continuous. This result contains a characterization of the DP property given in [3], answering a question of Pelczynski: E has the DP property if and only if any weakly...
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 topology on bounded sets. It is proved in [3] that bw(E) is a locally convex topology if and only if E is reflexive. In this paper we introduce the compact weak topology on a Banach space E, noted kw(E) or simply kw, as the finest topology that agrees with the weak topology on weakly compact subsets....
Compact and weakly compact homomorphisms between algebras of differentiable functions.
Many authors have recently studied compact and weakly compact homomorphisms between function algebras. Among them, Lindström and Llavona [2] treat weakly compact continuous homomorphisms between algebras of type C(T) when T is a completely regular Hausdorff space. Llavona asked wether the results in [2] are valid in the case of algebras of differentiable functions on Banach spaces. The purpose of this note is to give an affirmative answer to this question, by proving that weakly compact...
Integral polynomials on Banach spaces not containing
We give new characterizations of Banach spaces not containing in terms of integral and -dominated polynomials, extending to the polynomial setting a result of Cardassi and more recent results of Rosenthal.
Surjective factorization of holomorphic mappings
We characterize the holomorphic mappings between complex Banach spaces that may be written in the form , where is another holomorphic mapping and belongs to a closed surjective operator ideal.
Unconditionally converging holomorphic mappings between Banach spaces
Complemented copies of spaces in tensor products
We give sufficient conditions on Banach spaces and so that their projective tensor product , their injective tensor product , or the dual contain complemented copies of .
Secondary invariants for links
Polynomial invariants of boundary links
Polynomials and geometry of Banach spaces.
In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.
A note on Bayes estimates for exponential families.
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