Unconditionally converging polynomials on Banach spaces
Published online by Cambridge University Press: 24 October 2008
Extract
In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,
is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that
and
is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 2 , March 1995 , pp. 321 - 331
- Copyright
- Copyright © Cambridge Philosophical Society 1995
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