We give a necessary and sufficient condition on a positive compact operator T for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on l(infinity)(N) using tools of non standard analysis in an essential way. (C) 1996 Academic Press, Inc.

Albeverio, S., Guido, D., Ponosov, A., & Scarlatti, S. (1996). Singular traces and compact operators. JOURNAL OF FUNCTIONAL ANALYSIS, 137(2), 281-302 [10.1006/jfan.1996.0047].

Singular traces and compact operators

GUIDO, DANIELE;SCARLATTI, SERGIO
1996

Abstract

We give a necessary and sufficient condition on a positive compact operator T for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on l(infinity)(N) using tools of non standard analysis in an essential way. (C) 1996 Academic Press, Inc.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
positive compact operator; singular trace; ergodic states
Albeverio, S., Guido, D., Ponosov, A., & Scarlatti, S. (1996). Singular traces and compact operators. JOURNAL OF FUNCTIONAL ANALYSIS, 137(2), 281-302 [10.1006/jfan.1996.0047].
Albeverio, S; Guido, D; Ponosov, A; Scarlatti, S
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/43701
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