Factorization of weakly continuous holomorphic mappings

Details Factorization of weakly continuous holomorphic mappings Factorization of weakly continuous holomorphic mappings

1996-05-24

arxiv.org/abs/math/9605215v1

Studia Math. 118 (1996), 117-133

Mathematics

Functional Analysis

Scientific paper

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 {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es 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 $f$ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form $f=g\circ S$, where $S$ is a compact operator and $g$ a holomorphic mapping.

Affiliated with

Also associated with

No associations

Rating

Factorization of weakly continuous holomorphic mappings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Factorization of weakly continuous holomorphic mappings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorization of weakly continuous holomorphic mappings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-580701