Domingo García

REGULARITY AND ALGEBRAS OF ANALYTIC FUNCTIONS IN INFINITE DIMENSIONS

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).

Holomorphic mappings of bounded type

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.

THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

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

The Bishop-Phelps-Bollobás Theorem for bilinear forms

k

Estimates for the first and second Bohr radii of Reinhardt domains

of a Banach space, generalizing to

MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS

k

Two-dimensional Banach spaces with polynomial numerical index zero☆

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

Holomorphic Mappings of Bounded Type on (DF)-Spaces

k

The Bishop–Phelps–Bollobás Property: a Finite-Dimensional Approach

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

Analytic Structure in Fibers

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