Singular traces and compact operators

被引：27

作者：

Albeverio, S

Guido, D

Ponosov, A

Scarlatti, S

机构：

[1] SFB 237,ESSEN BOCHUM DUSSELDORF,GERMANY

[2] CERFIM,LOCARNO,SWITZERLAND

[3] UNIV ROMA TOR VERGATA,DIPARTIMENTO MATEMAT,I-00133 ROME,ITALY

[4] UNIV LAQUILA,DIPARTIMENTO MATEMAT,I-67100 LAQUILA,ITALY

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1996年 / 137卷 / 02期

关键词：

D O I：

10.1006/jfan.1996.0047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：281 / 302

页数：22