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Compact well-bounded operators

Published online by Cambridge University Press:  25 July 2002

Cheng Qingping  and
Ian Doust
Cheng Qingping
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA 6150, Australia e-mail: cheng@prodigal.murdoch.edu.au
Ian Doust
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia e-mail: i.doust@unsw.edu.au
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Every compact well-bounded operator has a representation as a linear combination of disjoint projections reminiscent of the representation of compact self-adjoint operators. In this note we show that the converse of this result holds, thus characterizing compact well-bounded operators. We also apply this result to study compact well-bounded operators on some special classes of Banach spaces such as hereditarily indecomposable spaces and certain spaces constructed by G. Pisier.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 3 , May 2001 , pp. 467 - 475
Copyright
2001 Glasgow Mathematical Journal Trust