[Banach] Abstract of a paper by Richard Skillicorn

This is an announcement for the paper "The uniqueness-of-norm problem for Calkin algebras" by Richard Skillicorn.

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).

Archive classification: math.FA

Submitted from: r.skillicorn@lancaster.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1507.08118

or

http://arXiv.org/abs/1507.08118