Speaker: Michiya Mori (RIKEN)

Title: On regular *-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras

Time/Date: 4:45-6:15pm, November 16 (Tue.), 2021

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract: In 1967, Richard Kadison posed a list of 20 open problems on operator algebras. Its 15th problem, which is apparently still open, is about a self-adjoint operator algebra each of whose self-adjoint operator has finite spectrum. It turns out that such an algebra, which I call an R*-algebra, can be characterized by means of seemingly unrelated conditions, like von Neumann regularity, closedness of the range of the operator, or uniqueness of C*-norm. I will explain the relation of R*-algebras to various other fields of mathematics, including lattice theory (particularly Boolean algebras and complemented modular lattices), inner product spaces (in connection with operator ranges and Banach space theory), and C*-/von Neumann algebras (with emphasis on AF algebras and the geometry of projections). This talk is based on the preprint arXiv:2107.05806. I will speak in Japanese, while the slides will be in English.