Journal of Operator Theory

Volume 66, Issue 2, Fall 2011 pp. 451-464.

The Baire property and the domain of iterates of a paracomplete linear relation

Authors: T. Alvarez (1) and D. Wilcox (2)
Author institution: (1) Department of Mathematics, University of Oviedo, 33007 Oviedo, Asturias, Spain
(2) Department of Mathematics and Applied Mathematics, University of Cape Town, 7700 Rondebosch, South Africa

Summary: The Baire category theorem for operators, concerning the denseness of the intersection of the ranges of certain sequences of continuous operators in Banach spaces, is generalized to multivalued linear operators. As an application we obtain a result which gives the denseness of the domains and ranges of certain sequences of paracomplete linear relations in Banach spaces. Results of Lennard and of Burlando about operators in Banach spaces are recovered.

Keywords: paracomplete linear relation, Baire property, lower essential resolvent set

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