ISSN:
1572-932X
Keywords:
Wijsman convergence
;
types on Banach spaces
;
weak* convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We introduce and study the notion of a distance type, on a Banach space, defined by a nested sequence of convex sets. Among other things, we show that there always exist distance types that are not types in the classical sense. Then, we recover the notion of the flat nested sequence of Milman and Milman and show that distance types defined by flat nested sequences coincide with the bidual types of Farmaki. These results are applied to show that a flat nested sequence of convex sets is Wijsman convergent to the intersection of their weak*-closures in bidual space.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008702707348
Permalink
