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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Well-bounded and scalar-type spectral operators on spaces not containing $ c\sb 0$


Author: Ian Doust
Journal: Proc. Amer. Math. Soc. 105 (1989), 367-370
MSC: Primary 47B40
DOI: https://doi.org/10.1090/S0002-9939-1989-0939963-X
MathSciNet review: 939963
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Abstract: It is known that a necessary and sufficient condition for a well-bounded operator on a weakly complete complex Banach space to be scalar-type spectral is that its decomposition of the identity be of bounded variation. We show in this paper that this condition is necessary and sufficient exactly when the Banach space does not contain a subspace isomorphic to $ {c_0}$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0939963-X
Keywords: Well-bounded operators, scalar-type spectral operators
Article copyright: © Copyright 1989 American Mathematical Society