Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some locally convex spaces of continuous vector-valued functions over a completely regular space and their duals


Author: A. Katsaras
Journal: Trans. Amer. Math. Soc. 216 (1976), 367-387
MSC: Primary 46E10
MathSciNet review: 0390733
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The strict, superstrict and the $ {\beta _F}$ topologies are defined on a space A of continuous functions from a completely regular space into a Banach space E. Properties of these topologies are discussed and the corresponding dual spaces are identified with certain spaces of operator-valued measures. In case E is a Banach lattice, A becomes a lattice under the pointwise ordering and the strict and superstrict duals of A coincide with the spaces of all $ \tau $-additive and all $ \sigma $-additive functionals on A respectively.


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

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0390733-9
PII: S 0002-9947(1976)0390733-9
Keywords: Locally convex spaces, strict topology, mixed topology, operator-valued measures, $ \sigma $-additive functionals, $ \tau $-additive functionals
Article copyright: © Copyright 1976 American Mathematical Society