Interpolation and Commutant Lifting with Weights

被引:0
作者
Good, Jennifer R. [1 ]
机构
[1] Univ Wisconsin Platteville, Dept Math, Platteville, WI 53818 USA
关键词
Nevanlinna-Pick interpolation; Commutant Lifting; Double Commutant; W*-correspondence; Noncommutative Hardy algebra; Sequence of Weights; ASTERISK-CORRESPONDENCES; ALGEBRAS; MODULES; REPRESENTATIONS; DILATIONS;
D O I
10.1007/s00020-017-2351-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Our two principle goals are generalizations of the commutant lifting theorem and the Nevanlinna-Pick interpolation theorem to the context of Hardy algebras built from W*-correspondences endowed with a sequence of weights. These theorems generalize theorems of Muhly and Solel from 1998 and 2004, respectively, which were proved in settings without weights. Of special interest is the fact that commutant lifting in our setting is a consequence of Parrott's Lemma; it is inspired by work of Arias.
引用
收藏
页码:349 / 389
页数:41
相关论文
共 22 条
[1]  
[Anonymous], THESIS
[2]  
[Anonymous], 2002, GRADUATE STUDIES MAT
[3]  
Arias A, 2004, J OPERAT THEOR, V52, P139
[4]   Noncommutative interpolation and Poisson transforms [J].
Arias, A ;
Popescu, G .
ISRAEL JOURNAL OF MATHEMATICS, 2000, 115 (1) :205-234
[5]  
BAILLET M, 1988, COMPOS MATH, V66, P199
[6]   Type I product systems of Hilbert modules [J].
Barreto, SD ;
Bhat, BVR ;
Liebscher, V ;
Skeide, M .
JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 212 (01) :121-181
[7]   Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras [J].
Davidson, KR ;
Pitts, DR .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1998, 31 (03) :321-337
[8]  
Lance E. C., 1995, Hilbert C*-Modules. A toolkit for operator algebraists, V210
[9]   Matricial Function Theory and Weighted Shifts [J].
Muhly, Paul S. ;
Solel, Baruch .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2016, 84 (04) :501-553
[10]   Tensor algebras over C*-correspondences: Representations, dilations, and C*-envelopes [J].
Muhly, PS ;
Solel, B .
JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 158 (02) :389-457