New classes of hermitian algebras

Are Austad (U Oslo)

May 05. 2025, 16:15 — 16:45

A locally compact group $G$ is said to be hermitian if the spectrum of any self-adjoint element of $L^1(G)$ is real. The study of when $L^1(G)$ is hermitian is a classical question and has its roots in Wiener's lemma. Losert's landmark result establishes this property for any compactly generated group of polynomial growth. By reframing the study of hermitianness of $L^1(G)$ in terms of existence of a derivation on $B(L^2(G))$, we prove by comparatively simple means that groups of strong subexponential growth are hermitian, generalizing Losert's result. Indeed, our technique gives rise to a procedure for proving hermitianness for Banach *-algebras appearing in (quantum) harmonic analysis. 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Harmonic Analysis (Workshop)
Organizer(s):
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)