The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are genrated by a "regular" operator, the answers change, namely such traces alway vanish on trace-class, non singularly traceable operators and axe always infinite on non trace-class, non singularly traceable operators. These results axe achieved on a general semifinite factor and make use of a new characterization of singular traceability (cf. [7]).

Guido, D., Isola, T. (2002). On the domain of singular traces. INTERNATIONAL JOURNAL OF MATHEMATICS, 13(6), 667-674 [10.1142/S0129167X02001447].

On the domain of singular traces

GUIDO, DANIELE;ISOLA, TOMMASO
2002-01-01

Abstract

The question whether an operator belongs to the domain of some singular trace is addressed, together with the dual question whether an operator does not belong to the domain of some singular trace. We show that the answers are positive in general, namely for any (compact, infinite rank) positive operator A we exhibit two singular traces, the first being zero and the second being infinite on A. However, if we assume that the singular traces are genrated by a "regular" operator, the answers change, namely such traces alway vanish on trace-class, non singularly traceable operators and axe always infinite on non trace-class, non singularly traceable operators. These results axe achieved on a general semifinite factor and make use of a new characterization of singular traceability (cf. [7]).
2002
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Ideals; Matuszewska indices; Semifinite factors; Singular traces; Spectral triples
Guido, D., Isola, T. (2002). On the domain of singular traces. INTERNATIONAL JOURNAL OF MATHEMATICS, 13(6), 667-674 [10.1142/S0129167X02001447].
Guido, D; Isola, T
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/43625
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