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Journal of the London Mathematical Society 1986 s2-34(3):479-488; doi:10.1112/jlms/s2-34.3.479
© 1986 by London Mathematical Society
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© Oxford University Press

Spectral Collapse

James W. Rowell

Department of Mathematics and Statistics, University of Minnesota, Duluth Duluth, Minnesota 55812-2496, USA

Following recent work of B. Barnes, we explore various conditions which guarantee inverse closure of a closed subalgebra of a unital Banach algebra. Noting the connection between inverse closure and collapse of the spectral lattice, we then salvage the hull-boundary relations which remain when the given subalgebra is not necessarily inverse closed. The results of the paper are then applied to determine the extent of spectral collapse in the special case of seminormal elements of a B*-algebra.


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