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Determinants associated to traces on operator bimodules | | K. Dykema
; F. Sukochev
; D. Zanin
; | | Date: |
2 May 2016 | | Abstract: | Given a II$_1$-factor $mathcal{M}$ with tracial state $ au$ and given an
$mathcal{M}$-bimodule $mathcal{E}(mathcal{M}, au)$ of operators affiliated
to $mathcal{M}$ and a trace $varphi$ on $mathcal{E}(mathcal{M}, au)$,
(namely, a linear functional that is invariant under unitary conjugation), we
prove that $det_varphi:mathcal{E}_{log}(mathcal{M}, au) o[0,infty)$
defined by $det_varphi(T)=exp(varphi(log |T|))$ is a multiplicative map on
the set $mathcal{E}_{log}(mathcal{M}, au)$ of all affiliated operators $T$
such that $log_+(|T|)inmathcal{E}(mathcal{M}, au)$. | | Source: | arXiv, 1605.0349 | | Services: | Forum | Review | PDF | Favorites | |
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