A Non-commutative Wiener-Wintner Theorem

Abstract

For a von Neumann algebra $\mathcal{M}$ with a faithful normal tracial state $\tau$ and a positive ergodic homomorphism $\alpha :{\mathcal{L}}^1(\mathcal{M},\tau )\to {\mathcal{L}}^1(\mathcal{M},\tau )$ such that $\alpha$ does not increase the norm in $\mathcal{M}$ and $\tau \circ \alpha =\tau$, we establish a non-commutative counterpart of the classical Wiener-Wintner Theorem.

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