Well-bounded operators on nonreflexive Banach spaces |
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| Authors: | Cheng Qingping Ian Doust |
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| 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 |
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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. |
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| Keywords: | Well-bounded operators functional calculus nonreflexive Banach spaces |
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