Local Spectral Theory of Linear Operators RS and SR

Benhida, Chafiq; Zerouali, E. H.

doi:10.1007/s00020-005-1375-3

Cited by 51 publications

(30 citation statements)

References 13 publications

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“…Thus, M z is a scalar operator of order m. We proved in [4] that for two given operators R and S, the operators RS and SR share the same local spectral properties (SVEP, (β), (β) , etc.) and almost all their global spectral properties.…”

Section: Introductionmentioning

confidence: 91%

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Backward Aluthge iterates of a hyponormal operator and scalar extensions

Benhida

Zerouali²

2009

Studia Math.

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Abstract. Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar. Introduction.Let H be a Hilbert space and L(H) be the algebra of bounded linear operators on H. We write σ(T ) for the spectrum of T .In [14], M. Putinar showed that a hyponormal operator has a scalar extension which means that it is similar to the restriction to an invariant subspace of a (generalized) scalar operator (in the sense of Colojoarǎ-Foiaş). This was extended to w-hyponormal operators by E. Ko [10].A bounded linear operator S on H is called scalar of order m if it has a spectral distribution of order m, i.e., if there is a continuous unital morphism of topological algebras Φ : C

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Section: Introductionmentioning

confidence: 91%

“…In [4], we proved that for two given operators R and S, the operators RS and SR have the same local spectral properties, in particular, the singlevalued extension property (SVEP). The following result shows that we have an analogue of the SVEP for Sobolev spaces.…”

Section: Subscalarity Of Rs and Srmentioning

confidence: 99%

Backward Aluthge iterates of a hyponormal operator and scalar extensions

Benhida

Zerouali²

2009

Studia Math.

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“…See [2,3] for example. We showed in [3] that RS and SR also share most of their local spectral properties. In particular, If RS has the single valued extension property (SV EP ) (resp.…”

Section: ) σ(Rs) \ {0} = σ(Sr) \ {0}mentioning

confidence: 99%

Spectral properties of commuting operations for 𝑛-tuples

Benhida

Zerouali

2011

Proc. Amer. Math. Soc.

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“…Also, Benhida and Zerouali proved that if T is p-hyponormal, loghyponormal or ω-hyponormal on a complex Hilbert space H, then T is subscalar. Moreover, E. Ko proved that every k-quasihyponormal operators are subscalar, see more details [4], [13] and [25]. Thus every hyponormal operator (k-quasihyponormal, ω-hyponormal) with finite spectrum is algebraic.…”

Section: Corollary 25 a Subscalar Operator With Finite Spectrum Is mentioning

confidence: 99%