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Well-bounded operators on nonreflexive Banach spaces
Authors:Cheng Qingping   Ian Doust
Affiliation:Department of Mathematics, Jingzhou Teachers College, Jingzhou, Hubei, People's Republic of China ; School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
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.

Keywords:Well-bounded operators   functional calculus   nonreflexive Banach spaces
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