@article {11638, title = {
Bimodules over vN(G), harmonic operators and  the non-commutative Poisson boundary.
}, journal = {Studia Mathematica}, volume = {249}, year = {2019}, pages = {193-213}, abstract = {Starting with a left ideal J of L1(G) we consider its annihilator J in L $\infty$ (G) and the generated VN(G)-bimodule in B(L 2 (G)), Bim(J ).
We prove that Bim(J ) = (Ran J) when G is weakly amenable discrete, compact
or abelian, where Ran J is a suitable saturation of J in the trace class.
We define jointly harmonic functions and jointly harmonic operators and show that,
for these classes of groups, the space of jointly harmonic operators is
the VN(G)-bimodule generated by the space of jointly harmonic functions.
Using this, we give a proof of the following result of Izumi and Jaworski {\textendash} Neufang: the non-commutative Poisson boundary is isomorphic to the crossed product of the space of harmonic functions by G.}, url = {https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/112628/bimodules-over-rm-vn-g-harmonic-operators-and-the-non-commutative-poisson-boundary}, author = {Anoussis, M. and Katavolos, A. and Todorov, I. G.} }