Singular traces are constructed on a general semifinite von Neumann algebra, thus generalizing the result of Dixmier (C.R. Acad. Sci. Paris 262, 1966.) Moreover our technique produces singular traces on type II1 factors. Such traces, though vanishing on all bounded operators, are non trivial on the *-algebra of affiliated unbounded operators. On a semifinite factor, we show that all traces are given by a dilation invariant functional on the cone of positive decreasing functions on [0, infinity), and we prove that the existence of a singular trace which is non trivial on a given operator is equivalent to an eccentricity condition on the singular values function, a result which generalizes the theorem given in (S. Albeverio, D. Guide, A. Ponosov, and S. Scarlatti, J. Funct. Anal., to appear.) for B(H). (C) 1995 Academic Press, Inc.

Guido, D., Isola, T. (1995). Singular Traces on Semifinite von Neumann Algebras. JOURNAL OF FUNCTIONAL ANALYSIS, 134(2), 451-485 [10.1006/jfan.1995.1153].

Singular Traces on Semifinite von Neumann Algebras

GUIDO, DANIELE;ISOLA, TOMMASO
1995-12-01

Abstract

Singular traces are constructed on a general semifinite von Neumann algebra, thus generalizing the result of Dixmier (C.R. Acad. Sci. Paris 262, 1966.) Moreover our technique produces singular traces on type II1 factors. Such traces, though vanishing on all bounded operators, are non trivial on the *-algebra of affiliated unbounded operators. On a semifinite factor, we show that all traces are given by a dilation invariant functional on the cone of positive decreasing functions on [0, infinity), and we prove that the existence of a singular trace which is non trivial on a given operator is equivalent to an eccentricity condition on the singular values function, a result which generalizes the theorem given in (S. Albeverio, D. Guide, A. Ponosov, and S. Scarlatti, J. Funct. Anal., to appear.) for B(H). (C) 1995 Academic Press, Inc.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
normal traces; Connes' non commutative geometry; Dixmier's construction; semifinite von Neumann algebras; invariant functional; cone of positive decreasing functions
Guido, D., Isola, T. (1995). Singular Traces on Semifinite von Neumann Algebras. JOURNAL OF FUNCTIONAL ANALYSIS, 134(2), 451-485 [10.1006/jfan.1995.1153].
Guido, D; Isola, T
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/43700
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