Well-bounded operators on nonreflexive Banach spaces
Qingping, C. and Doust, I. (1996) Well-bounded operators on nonreflexive Banach spaces. Proceedings of the American Mathematical Society, 124 (03). pp. 799-809.
*Subscription may be required
Abstract
Every well-bounded operator on a reflexive Banach space is of type (B), and hence has a nice integral representation with respect to a spectral family of projections. A longstanding open question in the theory of well-bounded operators is whether there are any nonreflexive Banach spaces with this property. In this paper we extend the known results to show that on a very large class of nonreflexive spaces, one can always find a well-bounded operator which is not of type (B). We also prove that on any Banach space, compact well-bounded operators have a simple representation as a combination of disjoint projections.
Item Type: | Journal Article |
---|---|
Murdoch Affiliation: | School of Mathematical and Physical Sciences |
Publisher: | American Mathematical Society |
Copyright: | © 1996 American Mathematical Society |
URI: | http://researchrepository.murdoch.edu.au/id/eprint/4877 |
![]() |
Item Control Page |
Downloads
Downloads per month over past year