if the dixmier trace of an operator A is defined as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{\sum_{i=0}^{N}\mu_{i}}{logN} [/tex] in the limit N-->oo (infinity)

where the eigenvalues are ordered in decreasing order

would not it better to be defined as

[tex] \frac{\sum_{i=0}^{N}\mu_{i}^{s}}{logN} [/tex]

here 's' is a parameter to be FIXED mathematically so

[tex] \sum_{i=0}^{N}\mu_{i}^{s}=T.log[/tex] then 'T' is just the Dixmier trace

the idea is to define the number 's' to be real of complex so the zeta function of operator A

[tex] Z=Tr(A^{s}) [/tex] has a pole or a logarithmic divergence , then the normal definition of dixmier trace is recovered when s=1

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# Question on Dixmier trace

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