Joint similarity and dilations for noncontractive sequences of operators
详细信息 查看全文
- 作者：Gheondea ; Aurelian ; Popescu ; Gelu
- 关键词：primary 47A48 ; 47A20 ; 47B50 ; secondary 47L25 ; 47D03 ; 46L07 ; Characteristic function ; Joint similarity ; Isometric dilation ; Fock space ; Free semigroup ; Noncontractive sequence
- 刊名：Journal of Functional Analysis
- 出版年：2003
- 出版时间：January 10, 2003
- 年：2003
- 卷：197
- 期：1
- 页码：68-109
- 全文大小：377 K
文摘
A characteristic function ΘT is defined, in terms of multianalytic operators on Fock spaces, for any noncontractive sequence T
(T1,…,Td) (d
N or d=∞) of operators on a Hilbert space H. It is shown that if ΘT is bounded, then it is unitarily equivalent to a compression of an orthogonal projection (on Krein spaces). This leads to a generalization of a theorem of Davis and Foiain spaces and Fourier representations for d-orthogonal shifts are obtained and used to study the geometry of the canonical minimal isometric dilation associated with a sequence T of operators on a Hilbert space.
(T1,…,Td) (dN or d=∞) of operators on a Hilbert space H. It is shown that if ΘT is bounded, then it is unitarily equivalent to a compression of an orthogonal projection (on Krein spaces). This leads to a generalization of a theorem of Davis and Foiain spaces and Fourier representations for d-orthogonal shifts are obtained and used to study the geometry of the canonical minimal isometric dilation associated with a sequence T of operators on a Hilbert space.