BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Baruch Solel (Technion - Israel Institute of Technology) DTSTART:20201202T113000Z DTEND:20201202T130000Z DTSTAMP:20260423T035823Z UID:WOTOA/14 DESCRIPTION:Title: I nvariant subspaces for certain tuples of operators\nby Baruch Solel (T echnion - Israel Institute of Technology) as part of Webinars on Operator Theory and Operator Algebras\n\n\nAbstract\nIn this talk we will generaliz e results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concern ing invariant subspaces for commuting tuples of operators. These authors p rove Beurling-Lax-Halmos type results for commuting tuples $T=(T_1\,\\ldot s\,T_d)$ operators that are contractive and pure\; that is $\\Phi_T(I)\\le q I$ and $\\Phi_T^n(I)\\searrow 0$ where $$\\Phi_T(a)=\\Sigma_i T_iaT_i^*. $$\n\nHere we generalize some of their results to commuting tuples $T$ sat isfying similar conditions but for $$\\Phi_T(a)=\\Sigma_{\\alpha \\in \\m athbb{F}^+_d} x_{|\\alpha|}T_{\\alpha}aT_{\\alpha}^*$$ where $\\{x_k\\}$ i s a sequence of non negative numbers satisfying some natural conditions (w here $T_{\\alpha}=T_{\\alpha(1)}\\cdots T_{\\alpha(k)}$ for $k=|\\alpha|$) . In fact\, we deal with a more general situation where each $x_k$ is repl aced by a $d^k\\times d^k$ matrix.\n\nWe also apply these results to subsp aces of certain reproducing kernel correspondences $E_K$ (associated with maps-valued kernels $K$) that are invariant under the multipliers given by the coordinate functions.\n LOCATION:https://researchseminars.org/talk/WOTOA/14/ END:VEVENT END:VCALENDAR