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)

 

 

Norm attaining operators and norming functionals


Authors: Russell G. Bilyeu and Paul W. Lewis
Journal: Proc. Amer. Math. Soc. 85 (1982), 245-250
MSC: Primary 28B05; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9939-1982-0652451-7
MathSciNet review: 652451
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The question of whether a countably additive measure with values in a Banach space attains the diameter of its range was unresolved. In this paper an example is given of a countably additive vector measure, taking values in a $ C(K)$ space, for which the diameter of the range is not attained. A property stronger than the attainment of the diameter, but which is possessed by many measures taking values in $ L$-spaces, is shown to fail for infinite-dimensional measures into a space having smooth dual. As an application of the concept of norming functional (the existence of which is equivalent to the attainment of diameter), a characterization is given of the countably additive measures into space having smooth dual.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28B05, 46G10

Retrieve articles in all journals with MSC: 28B05, 46G10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0652451-7
Article copyright: © Copyright 1982 American Mathematical Society