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SUMMARY:Mansi Suryawanshi (Technion - Israel Institute of Technology)
DTSTART:20260930T190000Z
DTEND:20260930T200000Z
DTSTAMP:20261001T102433Z
UID:NYC-NCG/226
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/226/
 ">Contractive Representations and Toeplitz-Type Realizations of the Odomet
 er Semigroup</a>\nby Mansi Suryawanshi (Technion - Israel Institute of Tec
 hnology) as part of Noncommutative geometry in NYC\n\n\nAbstract\nLet \\(\
 \mathcal O_n\\) denote the odometer semigroup. We study its\noperator-theo
 retic representations\, with particular emphasis on\ncontractive\, Nica-co
 variant\, and Fock-space representations. We describe\ndilation and subrep
 resentation phenomena for \\(\\mathcal O_n\\)\, and analyze\nthe associate
 d odometer maps \\(W_L\\) on vector-valued full Fock spaces.\nWe obtain a 
 canonical upper triangular decomposition in which the\nanalytic component 
 admits a Hardy-space realization as a Toeplitz\noperator \\(M_\\Theta\\). 
 This yields criteria for isometry\, unitarity\,\ninvertibility\, as well a
 s norm identities and Douglas-type factorization\nproperties. We also see 
 characterizations of Fredholmness and\nessential normality\, together with
  corresponding index and spectral\nconsequences.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/226/
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