1997/09/08 by Kenneth J. Dykema, Dykema, Kenneth J., Nigel J. Kalton +1
Mathematics · #47B10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B10
paper · pdf · doi:10.48550/arxiv.math/9709208
arxiv created 1997/09/08 · arxiv updated 2016/09/07
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.