Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 59-87.

Norm-closed bimodules of nest algebras

Authors: K.R. Davidson (1), A.P. Donsig (2), and T.D. Hudson (3)
Author institution: (1) Pure Math. Department, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada
(2) Dept. of Math. and Stats., University of Nebraska - Lincoln, Lincoln, NE 68508-0328, USA
(3) Department of Mathematics East Carolina University Greenville, NC 27834, USA

Summary: We study the support and essential support functions of a norm-closed bimodule of a nest algebra. An allowable support function pair determines a maximal bimodule. There is also a natural candidate for the minimal bimodule for a given support function pair. We determine precisely when this candidate is the minimal element. In the other cases, this module is still the intersection of all bimodules with a given support function pair, but it is not in this class itself.

Keywords: Nest algebra, bimodule, support, essential support, maximality, minimality

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