The spectra of general differential operators in the direct sum spaces

Sobhy El-sayed Ibrahim

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The paper is concerned with the spectral analysis for the class of linear operators $A = D_{λ} + X \otimes Y$ in non-archimedean Hilbert space, where $D_{λ}$ is a diagonal operator and $X \otimes Y$ is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.

On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator

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In the present work, using a formula describing all scalar spectral functions of a Carleman operator $A$ of defect indices $(1, 1)$ in the Hilbert space $L^{2} (X, μ)$ that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator $A$ .

Bounds for total antieigenvalue of a normal operator.

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

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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 $T^{* k} (| T ² | - | T * | ²) T^{k} \geq 0$ 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.