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Proceedings of the American Mathematical Society

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



Relative weak convergence in semifinite von Neumann algebras

Author: Victor Kaftal
Journal: Proc. Amer. Math. Soc. 84 (1982), 89-94
MSC: Primary 46L10
MathSciNet review: 633284
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Abstract: An operator is compact relative to a semifinite von Neumann algebra, i.e., belongs to the two-sided closed ideal generated by the finite projections relative to the algebra, if and only if it maps vector sequences converging weakly relative to the algebra into strongly converging ones (generalized Hilbert condition). The generalized Wolf condition characterizes the class of almost Fredholm operators.

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Keywords: Compact operator, almost Fredholm operator, relative weak convergence, Calkin algebra, Wolf Theorem, semifinite von Neumann algebra
Article copyright: © Copyright 1982 American Mathematical Society