Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Banach spaces of polynomials without copies of $ l\sp 1$

Author: Manuel Valdivia
Journal: Proc. Amer. Math. Soc. 123 (1995), 3143-3150
MSC: Primary 46G20; Secondary 46B20
MathSciNet review: 1273528
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X be a Banach space. For a positive integer m, let $ {\mathcal{P}_{{w^ \ast }}}{(^m}{X^ \ast })$ denote the Banach space formed by all m-homogeneous polynomials defined on $ {X^ \ast }$ whose restrictions to the closed unit ball $ B({X^ \ast })$ of $ {X^ \ast }$ are continuous for the weak-star topology. For each one of such polynomials, its norm will be the supremum of the absolute value in $ B({X^ \ast })$. In this paper the bidual of $ {\mathcal{P}_{{w^ \ast }}}{(^m}{X^ \ast })$ is constructed when this space does not contain a copy of $ {l^1}$. It is also shown that, whenever X is an Asplund space, $ {\mathcal{P}_{{w^ \ast }}}{(^m}{X^ \ast })$ is also Asplund.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G20, 46B20

Retrieve articles in all journals with MSC: 46G20, 46B20

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society