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]).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
