Joaquín M. Gutiérrez

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 injective operator ideal. Analogous results are previously obtained for multilinear mappings

Polynomial characterization of L∞-spaces

It is shown that, given an index m, a Banach space E is an L∞-space if and only if every 1-dominated m-homogeneous polynomial on E is integral. This extends a result for linear operators due to Stegall and Retherford.

The Dunford–Pettis property on tensor products

We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford–Pettis property (DPP). As a consequence, we obtain that ( c 0 &[otimes ]circ; π c 0 )** fails the DPP. Since ( c 0 &[otimes ]circ; π c 0 )* does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are [Lscr ] 1 -spaces, then E &[otimes ]circ; e has the DPP if and only if both E and F have the Schur property. Other results and examples are given.

Extensions of multilinear operators and Banach space properties

A new characterization of the Dunford-Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford-Pettis property and Pelczynskis property (V) are also found. Polynomial and holomorphic versions of these properties are given as well.

Polynomial Grothendieck properties

A Banach space

When every polynomial is unconditionally converging

E

Composition operators between algebras of differentiable functions

has the Grothendieck property if every (linear bounded) operator from

NUCLEAR AND INTEGRAL POLYNOMIALS

E

Schauder type theorems for differentiable and holomorphic mappings

into

Polynomials on banach spaces whose duals are isomorphic to ℓ 1 (Γ)

c_0