Displaying similar documents to “A perturbation characterization of compactness of self-adjoint operators”

Diagonals of Self-adjoint Operators with Finite Spectrum

Marcin Bownik, John Jasper (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).

On the generalized Kato spectrum

Benharrat, Mohammed, Messirdi, Bekkai (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 47A10. We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.

Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

Michael Gil (2012)

Annales UMCS, Mathematica

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We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.

Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

Michael Gil’ (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Jean Dolbeault, Maria Esteban, Eric Séré (2006)

Journal of the European Mathematical Society

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This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.