Matricial Function Theory and Weighted Shifts

被引:10
作者
Muhly, Paul S. [1 ]
Solel, Baruch [2 ]
机构
[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
关键词
Hardy algebras; Berezin transforms; Noncommutative analytic functions; Free holomorphic functions; Matricial sets; Matricial functions; Weighted shifts; ASTERISK-CORRESPONDENCES; INDUCED REPRESENTATIONS; TENSOR-ALGEBRAS; MODELS;
D O I
10.1007/s00020-016-2281-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let be the tensor algebra of a W*-correspondence E over a W*-algebra M. In earlier work, we showed that the completely contractive representations of , whose restrictions to M are normal, are parametrized by certain discs or balls indexed by the normal *-representations of M. Each disc has analytic structure, and each element gives rise to an operator-valued function on that is continuous and analytic on the interior. In this paper, we explore the effect of adding operator-valued weights to the theory. While the statements of many of the results in the weighted theory are anticipated by those in the unweighted setting, substantially different proofs are required. Interesting new connections with the theory of completely positive maps are developed. Our perspective has been inspired by work of Vladimir Muller (J Oper Theory 20(1):3-20, 1988) in which he studied operators that can be modeled by parts of weighted shifts. Our results may be interpreted as providing a description of operator algebras that can be modeled by weighted tensor algebras. Our results also extend work of Gelu Popescu (Mem Am Math Soc 200(941):vi+91, 2009), who investigated similar questions.
引用
收藏
页码:501 / 553
页数:53
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