MF-TRACES AND A LOWER BOUND FOR THE TOPOLOGICAL FREE ENTROPY DIMENSION IN UNITAL C*-ALGEBRAS

被引：3

作者：

Li, Qihui ^{[1
]}

Hadwin, Don ^{[2
]}

Li, Weihua ^{[3
]}

Shen, Junhao ^{[2
]}

机构：

[1] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

[2] Univ New Hampshire, Dept Math, Durham, NH 03824 USA

[3] Columbia Coll Chicago, Dept Sci & Math, Chicago, IL USA

来源：

JOURNAL OF OPERATOR THEORY | 2014年 / 71卷 / 01期

关键词：

Topological free entropy dimension; C*-algebra; noncommutative continuous function; free product; MF-trace; VON-NEUMANN-ALGEBRAS; FREE PROBABILITY-THEORY; PROPERTY T FACTORS; INFORMATION MEASURE; SUBALGEBRAS; SUBFACTORS; ANALOGS;

D O I：

10.7900/jot.2011oct16.1951

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We continue the work on topological free entropy dimension delta(top) from D. Hadwin, Q. Li, J. Shen, Topological free entropy dimensions in nuclear C*-algebras and in full free products of C*-algebras, Canad. J. Math. 63(2011), 551-590, D. Hadwin, J. Shen, Topological free entropy dimension in unital C*-algebras, J. Funct. Anal. 256(2009), 2027-2068, and D. Hadwin, J. Shen, Topological free entropy dimension. II, revised version. We introduce the notions of MF-trace, MF-ideal, and MF-nuclearity and use these concepts to obtain upper and lower bounds for delta(top), and in many cases we obtain an exact formula for delta(top). We also discuss semicontinuity properties of delta(top).

引用

页码：15 / 44

页数：30

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