Friday, April8, 2022 at 17:00 Athens time
Speaker: David Pitts (University of Nebraska-Lincoln, USA)
Title: Normalizers and Approximate Units for Inclusions of C*-Algebras
Abstract: Consider inclusions, which are pairs of C*-algebras (C, D) with D an abelian subalgebra of C. An element v ∈ C
normalizes D if v*Dv ∪ vDv* ⊆ D. The inclusion (C, D) is regular when the linear span of the normalizers is dense in C and is
singular when every normalizer belongs to D.
I will prove a commutation result for Hermitian normalizers, then discuss some consequences of this result related to familiar
constructions. Sample consequence: when D is a regular MASA in C, every approximate unit for D is an approximate unit for
C; this leads to simplifiation of the notions of Cartan MASA and C*-diagonal in the non-unital setting.
The inclusion (C, D) is intermediate to the regular MASA inclusion (B, D) if D ⊆ C ⊆ B. I will give examples showing some
singular MASA inclusions are intermediate to regular MASA inclusions, but others are not, and will discuss the fact that when
H is a separable, infinite dimensional Hilbert space, no MASA inclusion of the form (B(H), D) is intermediate to a regular MASA
inclusion.
Zoom meeting coordinates
upatras-gr.zoom.us/j/99245950296
or
Meeting ID: 992 4595 0296 Passcode: cstaralg
For additional information see the seminar webpage
