Domingo García

Richard M. Aron; Pablo Galindo; Domingo García; Manuel Maestre

A Banach space E is known to be Arens regular if every continuous linear mapping from E to E′ is weakly compact. Let U be an open subset of E, and letHb(U) denote the algebra of analytic functions on U which are bounded on bounded subsets of U lying at a positive distance from the boundary of U. We endow Hb(U) with the usual Frechet topology. Mb(U) denotes the set of continuous homomorphisms φ : Hb(U) → C. We study the relation between the Arens regularity of the space E and the structure of Mb(U).

Pablo Galindo; Domingo García; Manuel Maestre

Abstract For a Banach space E, we prove that the Frechet space H b(E) is the strong dual of an (LB)-space, B b(E), which leads to a linearization of the holomorphic mappings of bounded type. It is also shown that the holomorphic functions defined on (DFC)-spaces are of uniformly bounded type.

Yun Sung Choi; Domingo García; Sung Guen Kim; Manuel Maestre

In this paper, we introduce the polynomial numerical index of order

María D. Acosta; Julio Becerra-Guerrero; Domingo García; Manuel Maestre

k

Andreas Defant; Domingo García; Manuel Maestre

of a Banach space, generalizing to

Andreas Defant; Domingo García; Manuel Maestre

k

Domingo García; Bogdan C. Grecu; Manuel Maestre; Miguel Martín; Javier Merí

-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let

Pablo Galindo; Domingo García; Manuel Maestre

k

María D. Acosta; Julio Becerra Guerrero; Domingo García; Sun Kwang Kim; Manuel Maestre

be a positive integer. We then have the following: (i)

Javier Falcó; Domingo García; Manuel Maestre; Richard M. Aron

n^{(k)}(C(K))=1