Spectral properties of isometries of JB*-triples and C*-algebras

Abstract: A JB*-triple is a complex Banach space with a continuous non-associative triple product that satisfies specific axioms. Any C*-algebra can be seen as a JB*-triple with respect to the triple product defined using the algebra product and the involution. Surjective linear isometries of JB*-triples are closely related to the corresponding algebraic isomorphisms. 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, specifically 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 spectrum of a surjective linear isometry? The necessary conditions on such a set will be presented.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar