Canonical decompositions of completely nonunitary contractions

Levan, N.

doi:10.1016/0022-247x(84)90116-1

Cited by 8 publications

(6 citation statements)

References 2 publications

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“…As we have mentioned before that in [21], Levan showed that a c.n.u contraction could further be decomposed orthogonally into a c.n.i contraction and a unilateral shift (i.e., a pure contraction). We state the result below.…”

Section: Structure Theorems For γ N -Contractionsmentioning

confidence: 84%

“…[21],Theorem 1). With respect to a c.n.u contraction T and its adjoint T * on H, H admits the unique orthogonal decomposition…”

mentioning

confidence: 98%

“…In [21], Levan took an appealing next step to split further a c.n.u (completely non-unitary) contraction into two orthogonal parts of which one is a c.n.i (completely non-isometry) contraction and the other is a unilateral shift, i.e., a pure isometry.…”

mentioning

confidence: 99%

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Structure theorems for operators associated with two domains related to μ-synthesis

Bisai

Pal

2020

Bulletin des Sciences Mathématiques

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Section: Structure Theorems For γ N -Contractionsmentioning

confidence: 84%

“…[21],Theorem 1). With respect to a c.n.u contraction T and its adjoint T * on H, H admits the unique orthogonal decomposition…”

mentioning

confidence: 98%

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Structure theorems for operators associated with two domains related to μ-synthesis

Bisai

Pal

2020

Bulletin des Sciences Mathématiques

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“…H i (T * ) is also the largest T * -invariant subspace on which T is a co-isometry (cf. [22]). A contraction T is said to be a completely non co-isometric (c.n.c.)…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Pairs of Commuting Pure Contractions and Isometric dilation

Sarkar

2021

Preprint

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A particular case of the fundamental Sz.-Nagy-Foias functional model for a contraction states that a pure contraction always dilates to a pure isometry. We are interested in the similar question for pairs, more precisely: does a pair of commuting pure contractions always dilate to a pair of commuting pure isometries? The purpose of this article is to identify pairs of commuting pure contractions for which the above question has an affirmative answer. Our method is based on an explicit structure of isometric dilation for pure pairs of commuting contractions obtained in a recent work by Das, Sarkar and the author.

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“…., S n−1 , P) in literature, plays lead role in every section of operator theory on the symmetrized polydisc. In [10], Levan proved that a c.n.u contraction can further be decomposed into a unilateral shift and a cn.i contraction. Using Levan's decomposition of a c.n.u contraction we have a model for c.n.u contraction.…”

Section: Introductionmentioning

confidence: 99%

A Nagy-Foias program for a c.n.u. $Γ_n$-contraction

Bisai¹,

Pal²

2021

Preprint

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as a spectral set is called a Γ n -contraction. We construct a minimal Γ n -isometric dilation for a particular class of c.n.u. Γ n -contractions and hence express a c.n.u.for some operator C i . We also produce an abstract model for a particular class of c.n.u. Γ n -contractions. We provide an example to show that such non-commutative model does not exists for any c.n.u. Γ n -contraction. By an application of this model we obtain a complete unitary invariant for such c.n.u. Γ ncontraction. The entire program is based on Nagy-Foias model theory for a c.n.u. contraction.

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Canonical decompositions of completely nonunitary contractions

Cited by 8 publications

References 2 publications

Structure theorems for operators associated with two domains related to μ-synthesis

Structure theorems for operators associated with two domains related to μ-synthesis

Pairs of Commuting Pure Contractions and Isometric dilation

A Nagy-Foias program for a c.n.u. $Γ_n$-contraction

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