In this paper, we study the relation between local spectral properties of the linear operators RS and SR. We show that RS and SR share the same local spectral properties SVEP, (β), (δ) and decomposability. We also show that RS is subscalar if and only if SR is subscalar. We recapture some known results on spectral properties of Aluthge transforms.
For A ∈ L(X), B ∈ L(Y ) and C ∈ L(Y, X) we denote by M C the operator defined on X ⊕ Y by A C 0 B . In this article, we study defect set D Σ = (Σ(A) ∪ Σ(B)) \ Σ(M C ) for different spectra including the spectrum, the essential spectrum, Weyl spectrum and the approximate point spectrum. We then apply the obtained results to the stability of such spectra (D Σ = ∅) and the classes of operators C for which stability holds of M C using local spectral theory.
The aim of this paper is to study properties of sequences that are recursively de ned by a linear equation and their applications to the truncated moment problem in connection with the problem of subnormal completion of the truncated weighted shifts. Special cases are considered and some classical results due to Stamp i, Curto and Fialkow are recovered using elementary techniques.
Abstract. Let R and S be commuting n-tuples. We give some spectral and local spectral relations between RS and SR. In particular, we show that RS has the single valued extension property or satisfies Bishop's property (β) if and only if SR has the corresponding property.
Let R and S be commuting n-tuples of operators. We will give some spectral relations between RS and SR that extend the case of single operators. We connect the Taylor spectrum, the Fredholm spectrum and some other joint spectra of RS and SR. Applications to Aluthge transforms of commuting n-tuples are also provided.
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