Displaying similar documents to “On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator”

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.

Isolated points of spectrum of k-quasi-*-class A operators

Salah Mecheri (2012)

Studia Mathematica

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Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class, denoted *, of operators satisfying T * k ( | T ² | - | T * | ² ) T k ≥ 0 where k is a natural number, and we prove basic structural properties of these operators. Using these results, we also show that if E is the Riesz idempotent for a non-zero isolated point μ of the spectrum of T ∈ *, then E is self-adjoint and EH = ker(T-μ) = ker(T-μ)*. Some spectral properties are also presented.

Local spectrum and local spectral radius of an operator at a fixed vector

Janko Bračič, Vladimír Müller (2009)

Studia Mathematica

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Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with σ T ( e ) = σ δ ( T ) , respectively r T ( e ) = r ( T ) , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.