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...r(A\Delta^{-s})$, with $\Delta$ the [[Laplace operator]]. It satisfies the trace condition: $\mathrm{res}(AB) = \mathrm{res}(BA)$. A very important property ...[[elliptic operator]], $n \in \mathbf{N}$), it coincides with the Dixmier trace, and one has

A non-zero lower semi-continuous semi-finite trace $ f $ satisfying the following condition (cf. [[Trace on a C*-algebra|Trace on a $ C ^ {*} $-

...ann algebra of this Hilbert algebra is isomorphic to $\mathfrak A$ and the trace determined by the Hilbert algebra on $\mathfrak A$ coincides with the initi <table><TR><TD valign="top">[1]</TD> <TD valign="top"> J. Dixmier, "Les algèbres d'opérateurs dans l'espace hilbertien: algèbres de von

one usually considers the trace of the operator. Let $ A $ be a faithful normal semi-finite trace on $ \mathfrak A $

A trace $ f $ be a trace on $ A $,

''Dixmier map'' ...bit method|orbit method]] of A.A. Kirillov [[#References|[a12]]]. In 1966, Dixmier extended his definition to solvable Lie algebras [[#References|[a7]]] (here

be the [[Trace|trace]] of the operator $ T _ {x} ^ {( \alpha ) } T _ {x} ^ {( \alpha )* } $. ...ress (1968)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> J. Dixmier, "<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.o

is called a trace if $ \phi ( U T U ^ {-1} ) = \phi ( T) $ A trace is said to be finite if $ \phi ( T) &lt; \infty $

is the faithful normal semi-finite trace $ t $( cf. [[Trace on a C*-algebra|Trace on a $ C ^ {*} $-

...under certain additional conditions, a $\Cstar$-algebra with a continuous trace may be represented as the algebra of vector functions on its spectrum $\h |valign="top"|{{Ref|Di}}||valign="top"| J. Dixmier, "$\Cstar$ algebras", North-Holland (1977) (Translated from French) {{MR|0

...r algebras, as founded by J. von Neumann and developed by M.A. Naimark, J. Dixmier, R.V. Kadison [[#References|[a1]]], M. Tomita, M. Takesaki [[#References|[a with trace 1. Some interesting random variables are the positions and momenta of the p

...ally proved before the discoveries above in [[#References|[a15]]], using a trace formula which shows that every non-zero $ A _ {1} ( K) $- ...308.17007}} </TD></TR><TR><TD valign="top">[a12]</TD> <TD valign="top"> J. Dixmier, "Sur les algèbres de Weyl II" ''Bull. Sci. Math.'' , '''94''' (1970) pp.