JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Factorization of weakly continuous holomorphic mappings

### Tom 118 / 1996

Studia Mathematica 118 (1996), 117-133 DOI: 10.4064/sm-118-2-117-133

#### Streszczenie

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 uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ƒ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f = g∘S, where S is a compact operator and g a holomorphic mapping.

#### Autorzy

• Manuel González

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek