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Journal of Operator Theory

Volume 37, Issue 1, Winter 1997  pp. 35-50.

The dual theory of well-bounded operators

Authors: Qingping Cheng (1) and Ian Doust (2)
Author institution:(1) School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA 6150, AUSTRALIA
(2) School of Mathematics, University of New South Wales, Sydney, NSW 2052, AUSTRALIA

Summary: The adjoint of a well-bounded operator is also well-bounded, but in general the hoped for natural relationship between the corresponding decompositions of the identity do not hold if the underlying Banach space is nonreflexive. In this paper we discuss the conditions under which the adjoint family of a decomposition of the identity forms a decomposition of the identity for the adjoint of a well-bounded operator.

Keywords: Well-bounded operators, decompositions of the identity.

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