English

The uniqueness-of-norm problem for Calkin algebras

Functional Analysis 2016-02-16 v1

Abstract

We examine the question of whether the Calkin algebra of a Banach space must have a unique complete algebra norm. We present a survey of known results, and make the observation that a recent Banach space construction of Argyros and Motakis (preprint, 2015) provides the first negative answer. The parallel question for the weak Calkin algebra also has a negative answer; we demonstrate this using a Banach space of Read (J. London Math. Soc. 1989).

Keywords

Cite

@article{arxiv.1507.08118,
  title  = {The uniqueness-of-norm problem for Calkin algebras},
  author = {Richard Skillicorn},
  journal= {arXiv preprint arXiv:1507.08118},
  year   = {2016}
}