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Canonical decomposition of a tetrablock contraction and operator model.
- Source :
-
Journal of Mathematical Analysis & Applications . Jun2016, Vol. 438 Issue 1, p274-284. 11p. - Publication Year :
- 2016
-
Abstract
- A triple of commuting operators for which the closed tetrablock E ‾ is a spectral set is called a tetrablock contraction or an E -contraction. The set E is defined as E = { ( x 1 , x 2 , x 3 ) ∈ C 3 : 1 − z x 1 − w x 2 + z w x 3 ≠ 0 whenever | z | ≤ 1 , | w | ≤ 1 } . We show that every E -contraction can be uniquely written as a direct sum of an E -unitary and a completely non-unitary 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 438
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 113236884
- Full Text :
- https://doi.org/10.1016/j.jmaa.2016.02.027