BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elias G. Katsoulis (East Carolina University) DTSTART:20230419T190000Z DTEND:20230419T200000Z DTSTAMP:20260420T053057Z UID:NYC-NCG/128 DESCRIPTION:Title: Isomorphisms and stable isomorphisms of non-selfadjoint operator algebra s\nby Elias G. Katsoulis (East Carolina University) as part of Noncomm utative geometry in NYC\n\n\nAbstract\nIn this talk we address isomorphism s and stable isomorphisms of various\nclasses of operator algebras. We sta te and resolve the isomorphism problem for\ntensor algebras of unital mult ivariable dynamical systems. Specifically we show\nthat unitary equivalenc e after a conjugation for multi-variable dynamical systems\nis a complete invariant for complete isometric isomorphisms between their tensor\nalgebr as. In particular\, this settles a conjecture of Davidson and Kakariadis r elating\nto work of Arveson from the sixties\, and extends related work of Kakariadis and\nKatsoulis.\n\nWe also address stable isomorphism of opera tor algebras\, in connection with a\nrecent work of Dor-On\, Eilers and Ge ffen. Among others we show that if $\\mathcal{A}$\n and $\\mathcal{B}$ are operator algebras with diagonals isomorphic to $c_0$ and \n$\\mathcal{K}$ are the compact\noperators\, then $\\mathcal{A}\\otimes\\mathcal{K}$ and $\\mathcal{B}\\otimes\\mathcal{K}$\nare isometrically isomorphic if and on ly if $\\mathcal{A}$ and\n$\\mathcal{B}$ are isometrically isomorphic. If the algebras $\\mathcal{A}$ and $\\mathcal{B}$ satisfy an extra analyticit y\ncondition\, a similar result holds with $\\mathcal{K}$ being replaced b y any operator algebra\ncontaining the compact operators. Time permitting we will discuss other classes\nof operator algebras and their stable isomo rphisms\, including tensor algebras of\nmultivariable dynamical systems.\n \nThe above results come from various projects with C. Ramsey\, E. Kakaria dis\nand X. Lin.\n LOCATION:https://researchseminars.org/talk/NYC-NCG/128/ END:VEVENT END:VCALENDAR