English

Spectral characterization of sums of commutators II

Functional Analysis 2016-09-07 v1

Abstract

For countably generated ideals, \Jc\Jc, of B(\Hil)B(\Hil), geometric stability is necessary for the canonical spectral characterization of sums of (\Jc,B(\Hil))(\Jc,B(\Hil))--commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, \Jc\Jc, having quasi--nilpotent elements that are not sums of (\Jc,B(\Hil))(\Jc,B(\Hil))--commutators. Also, every trace on every geometrically stable ideal is a spectral trace.

Keywords

Cite

@article{arxiv.math/9709208,
  title  = {Spectral characterization of sums of commutators II},
  author = {Kenneth J. Dykema and Nigel J. Kalton},
  journal= {arXiv preprint arXiv:math/9709208},
  year   = {2016}
}