Spectral characterization of sums of commutators II

Details Spectral characterization of sums of commutators II Spectral characterization of sums of commutators II

1997-09-08

arxiv.org/abs/math/9709208v1

Mathematics

Functional Analysis

Scientific paper

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

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