Relative weak convergence in semifinite von Neumann algebras

Kaftal, Victor

doi:10.1090/S0002-9939-1982-0633284-4

Relative weak convergence in semifinite von Neumann algebras
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Proc. Amer. Math. Soc. 84 (1982), 89-94 Request permission

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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