Kenneth J. Dykema, Nigel J. Kalton
Published 1997-09-08Version 1
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.
Spectral characterization of sums of commutators I
Commutators on $L_p$, $1\le p<\infty$
Commutators on $\ell_{\infty}$
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