POISSON TRANSFORM FOR HIGHER-RANK GRAPH ALGEBRAS AND ITS APPLICATIONS

被引：0

作者：

Skalski, Adam ^{[1
,2
]}

Zacharias, Joachim ^{[3
]}

机构：

[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

[2] Univ Lodz, Dept Math, PL-90238 Lodz, Poland

[3] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

JOURNAL OF OPERATOR THEORY | 2010年 / 63卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Higher-rank graphs; graph operator algebras; dilation; commutant lifting; pure states; C-ASTERISK-ALGEBRAS; CUNTZ-KRIEGER ALGEBRAS; ISOMETRIC DILATIONS; TOEPLITZ ALGEBRAS; PRODUCT SYSTEMS; REPRESENTATIONS; OPERATORS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying relations encoded by the graph structure which we call Lambda-contractions or Lambda-isometries. Besides commutant lifting results and characterisations of pure states on higher rank graph algebras several applications to the structure theory of non-selfadjoint graph operator algebras are presented generalising recent results in special cases.

引用

页码：425 / 454

页数：30

共 26 条

[1]

[Anonymous], 1992, MONOGRAPHS MATH

[2] Subalgebras of C*-algebras III: Multivariable operator theory [J].

Arveson, W .

ACTA MATHEMATICA, 1998, 181 (02) :159-228

[3]

Arveson W., 1969, Acta Math, V123, P141, DOI 10.1007/BF02392388

[4] Minimal Cuntz-Krieger dilations and representations of Cuntz-Krieger algebras [J].

Bhat, B. V. Rajarama ;

Dey, Santanu ;

Zacharias, Joachim .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2006, 116 (02) :193-220

[5]

Bratteli O, 2000, J OPERAT THEOR, V43, P97

[6] The algebraic structure of non-commutative analytic Toeplitz algebras [J].

Davidson, KR ;

Pitts, DR .

MATHEMATISCHE ANNALEN, 1998, 311 (02) :275-303

[7]

DAVIDSON KR, J OPERATOR IN PRESS

[8]

Dey S., 2007, Colloq. Math, V107, P141, DOI DOI 10.4064/CM107-1-12

[9] PARTIALLY ISOMETRIC DILATIONS OF NONCOMMUTING N-TUPLES OF OPERATORS [J].

Jury, Michael T. ;

Kribs, David W. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (01) :213-222

[10]

KRIBS DAVID W., 2006, Math. Proc. R. Ir. Acad., V106A, P199, DOI [10.1353/mpr.2006.0002.452, DOI 10.1353/MPR.2006.0002.452]

← 1 2 3 →