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

Mercer, Richard

doi:10.1090/S0002-9939-1985-0784174-0

Convergence of Fourier series in discrete crossed products of von Neumann algebras
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Proc. Amer. Math. Soc. 94 (1985), 254-258 Request permission

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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