Some Calkin algebras have outer automorphisms

TL;DR

This paper investigates certain quotient C*-algebras of bounded operators on nonseparable Hilbert spaces and demonstrates, under set-theoretic assumptions, the existence of many outer automorphisms.

Contribution

It shows that some Calkin algebras on nonseparable Hilbert spaces have numerous outer automorphisms, highlighting new structural properties.

Findings

Existence of many outer automorphisms in certain Calkin algebras

Consistent set-theoretic conditions influence automorphism structure

Extension of automorphism results to nonseparable cases

Abstract

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.