Well-bounded operators on nonreflexive Banach spaces

C. Qingping; I. Doust

doi:10.1090/S0002-9939-96-03098-5

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Well-bounded operators on nonreflexive Banach spaces

Journal article

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Well-bounded operators on nonreflexive Banach spaces

C. Qingping and I. Doust

Proceedings of the American Mathematical Society, Vol.124(03), pp.799-809

1996

DOI: https://doi.org/10.1090/S0002-9939-96-03098-5

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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.

Details

Title: Well-bounded operators on nonreflexive Banach spaces
Authors/Creators: C. Qingping (Author/Creator) - Department of Mathematics, Jingzhou Teachers College, Jingzhou, Hubei, People’s Republic of China
I. Doust (Author/Creator) - UNSW Sydney
Publication Details: Proceedings of the American Mathematical Society, Vol.124(03), pp.799-809
Publisher: American Mathematical Society
Identifiers: 991005542742407891
Murdoch Affiliation: School of Mathematical and Physical Sciences
Language: English
Resource Type: Journal article

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