BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Aristides Katavolos (University of Athens) DTSTART:20210224T200000Z DTEND:20210224T210000Z DTSTAMP:20260420T052739Z UID:NYC-NCG/41 DESCRIPTION:Title: Harmonic functions\, crossed products and approximation properties\nb y Aristides Katavolos (University of Athens) as part of Noncommutative geo metry in NYC\n\n\nAbstract\nThe space of harmonic functions on a locally c ompact group $G$ is the fixed point space of a\ncertain Markov operator. I ts `quantization'\, the corresponding fixed point space of operators on $L ^2(G)$\, coincides with the weak-* closed bimodule over the group von Neum ann algebra generated by this space. We examine the analogous spaces of jo intly harmonic functions\nand their quantized operator bimodules. This lea ds to two different notions of crossed product of operator spaces by actio ns of $G$\, which coincide when $G$ satisfies a certain approximation prop erty. The corresponding (dual) notions of crossed products of (co-) action s by the von Neumann algebra of $G$ always coincide. This gives a new appr oach to the correspondence between spectral synthesis and operator synthes is.\n\n\nThe talk is a survey of joint work with M. Anoussis and I.G. Todo rov\, and of recent work by D. Andreou.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/41/ END:VEVENT END:VCALENDAR