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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Essential central range and selfadjoint commutators in properly infinite von Neumann algebras


Author: Herbert Halpern
Journal: Trans. Amer. Math. Soc. 228 (1977), 117-146
MSC: Primary 46L10
MathSciNet review: 0430802
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Abstract: The essential central range of an element A of a von Neumann algebra with respect to a central ideal is characterized as those elements arbitrarily close to the compression of A to a subspace large with respect to the ideal. The selfadjoint commutators in a properly infinite algebra are shown to be the elements whose essential central ranges with respect to the strong radical contain 0.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0430802-9
Keywords: Essential central spectrum, selfadjoint commutators
Article copyright: © Copyright 1977 American Mathematical Society