Event Details
Conferenciante: Prof. Dijana Ilišević. (Universidad de Zagreb)
Título: Isometries of JB*-triples and C*-algebras,
their eigenprojections and eigenvalues
Fecha y hora: 14 de junio de 2024, 11:00.
Lugar: Seminario 2, IMAG
Resumen: A JB*-triple is a remarkable structure in which surjective linear isometries are associated with corresponding algebraic isomorphisms. Some important JB*-triples are: (matrix and) operator spaces B(H,K) of bounded linear operators from a complex Hilbert space H to a complex Hilbert space K, A(H) of skew-symmetric operators on H, and S(H) of symmetric operators on H, C*-algebras, etc. The aim of this talk is to recall and connect some recent and not so recent results on the structure of surjective isometries of JB*-triples, specially C*-algebras, following a long line of work starting with the celebrated Banach-Stone theorem. Attention will be focused on periodic isometries, their eigenprojections and eigenvalues. They will be studied in connection with the following inverse eigenvalue problem for isometries: when is a given finite set of modulus one complex numbers the spectrum of a surjective linear isometry? The necessary conditions on such a set will be presented. Special emphasis will be given to C0(Ω), the Banach space of continuous complex-valued functions on a connected locally compact Hausdorf space Ω, vanishing at infinity.
