Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Weak topologies on subspaces of $ C(S)$

Author: Joel H. Shapiro
Journal: Trans. Amer. Math. Soc. 157 (1971), 471-479
MSC: Primary 46E10
MathSciNet review: 0415285
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ S$ be a locally compact Hausdorff space, $ E$ a linear subspace of $ C(S)$. It is shown that the unit ball of $ E$ is compact in the strict topology if and only if both of the following two conditions are satisfied: (1) $ E$ is the Banach space dual of $ M(S)/{E^0}$ in the integration pairing, and (2) the bounded weak star topology on $ E$ coincides with the strict topology. This result is applied to several examples, among which are $ {l^\infty }$ and the space of bounded analytic functions on a plane region.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E10

Retrieve articles in all journals with MSC: 46E10

Additional Information

Keywords: Bounded continuous functions, bounded weak star topology, strict topology, equicontinuous set, bounded analytic functions, Lipschitz spaces
Article copyright: © Copyright 1971 American Mathematical Society