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Convergence of Fourier series in discrete crossed products of von Neumann algebras

Author: Richard Mercer
Journal: Proc. Amer. Math. Soc. 94 (1985), 254-258
MSC: Primary 46L10; Secondary 47C15
MathSciNet review: 784174
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Abstract: The convergence of the generalized Fourier series $ \Sigma \pi (x(g))u(g)$ is considered in the crossed product of a von Neumann algebra by a discrete group. An example from classical theory shows that this series does not converge in any of the usual topologies. It is proven that this series does converge in a topology introduced by Bures which is well suited to a crossed product situation. As an elementary application, we answer the question: In what topology is an infinite matrix (representing a bounded operator) the sum of its diagonals?

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Keywords: Discrete crossed product, conditional expectation
Article copyright: © Copyright 1985 American Mathematical Society

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