Bimodules over $\mathrm{VN}(G)$, harmonic operators and the non-commutative Poisson boundary

Mihalis Anoussis, Aristides Katavolos, Ivan G. Todorov

Starting with a left ideal $J$ of $L^1(G)$ we consider its annihilator $J^{\perp }$ in $L^{\infty }(G)$ and the generated $\mathrm{VN}(G)$-bimodule in $\mathcal{B}(L^2(G))$, ${\rm Bim}(…