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Canonical decomposition of a tetrablock contraction and operator model
- Publication Year :
- 2015
-
Abstract
- A triple of commuting operators for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set is called a tetrablock contraction or an $\mathbb E$-contraction. The set $\mathbb E$ is defined as \[ \mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\, 1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}. \] We show that every $\mathbb E$-contraction can be uniquely written as a direct sum of an $\mathbb E$-unitary and a completely non-unitary $\mathbb E$-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions.<br />Comment: To appear in Journal of Mathematical Analysis and Applications
- Subjects :
- Mathematics - Functional Analysis
Mathematics - Operator Algebras
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1504.02981
- Document Type :
- Working Paper