<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Anoussis, M.</style></author><author><style face="normal" font="default" size="100%">Katavolos, A.</style></author><author><style face="normal" font="default" size="100%">Todorov, I. G.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">&lt;pre&gt;&lt;span style=&quot;font-family: Times New Roman, Times, serif;&quot;&gt;Bimodules over vN(G), harmonic operators and  the non-commutative Poisson boundary.&lt;/span&gt;&lt;/pre&gt;</style></title><secondary-title><style face="normal" font="default" size="100%">Studia Mathematica</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">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</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">249</style></volume><pages><style face="normal" font="default" size="100%">193-213</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Starting with a left ideal J of L&lt;sup&gt;1&lt;/sup&gt;(G) we consider its annihilator J&lt;sup&gt; ⊥&lt;/sup&gt; in L&lt;sup&gt; ∞&lt;/sup&gt; (G) and the generated VN(G)-bimodule in B(L&lt;sup&gt; 2&lt;/sup&gt; (G)), Bim(J&lt;sup&gt; ⊥&lt;/sup&gt; ).&lt;br&gt; We prove that Bim(J&lt;sup&gt; ⊥&lt;/sup&gt; ) = (Ran J)&lt;sup&gt; ⊥&lt;/sup&gt; when G is weakly amenable discrete, compact &lt;br&gt;or abelian, where Ran J is a suitable saturation of J in the trace class. &lt;br&gt;We define jointly harmonic functions and jointly harmonic operators and show that, &lt;br&gt;for these classes of groups, the space of jointly harmonic operators is &lt;br&gt;the VN(G)-bimodule generated by the space of jointly harmonic functions. &lt;br&gt;Using this, we give a proof of the following result of Izumi and Jaworski – Neufang: the non-commutative Poisson boundary is isomorphic to the crossed product of the space of harmonic functions by G.</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record></records></xml>