A Non-commutative Wiener-Wintner Theorem

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

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