BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilja Gogić (University of Zagreb\, Croatia) DTSTART:20251013T150000Z DTEND:20251013T160000Z DTSTAMP:20260423T035715Z UID:ENAAS/144 DESCRIPTION:Title: Spectrum-shrinking maps and nonlinear preservers on matrix domains\nby Ilja Gogić (University of Zagreb\, Croatia) as part of European Non-Asso ciative Algebra Seminar\n\n\nAbstract\nThe celebrated Kaplansky–Aupetit conjecture asks whether\nevery surjective linear map between unital semisi mple Banach algebras\nthat shrinks the spectrum must be a Jordan homomorph ism. While the\nconjecture has been resolved in specific settings (most no tably for\nvon Neumann algebras by Aupetit and for algebras of bounded lin ear\noperators on Banach spaces by Sourour)\, it remains widely open\, eve n\nfor C*-algebras. In contrast\, spectrum-preserving maps are often more\ naccessible\, and a natural question is whether results in that setting\nc an be extended to the spectrum-shrinking case. However\, existing\nresults indicate that such generalizations are typically far more\ndelicate. Moti vated by this\, the talk investigates continuous\nspectrum-shrinking maps from various subsets Xₙ of the complex matrix\nalgebra Mₙ with values in another matrix algebra Mₘ. The classes of\ndomains Xₙ under conside ration include structural matrix algebras\n(i.e. subalgebras of Mₙ conta ining all diagonal matrices)\, the sets of\nnormal and singular matrices\, and matrix Lie groups such as GL(n)\,\nSL(n)\, and U(n). Our first object ive is to determine when such\nspectrum-shrinking maps automatically prese rve the spectrum. Building\non this\, and Šemrl’s influential nonlinear characterization of Jordan\nautomorphisms of Mₙ (when n ≥ 3) as conti nuous maps preserving both\nspectrum and commutativity\, our second object ive is to establish an\nanalogous nonlinear preserver theorem for maps X ₙ → Mₙ. This is based\non joint work with Alexandru Chirvasitu (Univ ersity at Buffalo) and\nMateo Tomašević (University of Zagreb).\n LOCATION:https://researchseminars.org/talk/ENAAS/144/ END:VEVENT END:VCALENDAR