Wellbounded operators on nonreflexive Banach spaces
Authors:
Cheng Qingping and Ian Doust
Journal:
Proc. Amer. Math. Soc. 124 (1996), 799808
MSC (1991):
Primary 47B40; Secondary 46B10, 46B15, 46B20, 47A60
MathSciNet review:
1301522
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Abstract: Every wellbounded 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 wellbounded 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 wellbounded operator which is not of type (B). We also prove that on any Banach space, compact wellbounded operators have a simple representation as a combination of disjoint projections.
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Additional Information
Cheng Qingping
Affiliation:
Department of Mathematics, Jingzhou Teachers College, Jingzhou, Hubei, People’s Republic of China
Email:
i.doust@unsw.edu.au
Ian Doust
Affiliation:
School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Email:
cheng@prodigal.murdoch.edu.au
DOI:
http://dx.doi.org/10.1090/S0002993996030985
PII:
S 00029939(96)030985
Keywords:
Wellbounded operators,
functional calculus,
nonreflexive Banach spaces
Received by editor(s):
August 29, 1994
Additional Notes:
This research was supported by the Australian Research Council.
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1996
American Mathematical Society
