Quasi-nilpotent perturbations of the generalized Kato spectrum
-
Mohammed Benharrat
and
Bekkai Messirdi
Abstract
In this paper, we show that the generalized Kato spectrum of a bounded operator in a Banach space is invariant under perturbation by commuting quasi-nilpotent operators, and the Kato spectrum is stable under additive commuting nilpotent perturbations. Our results are used to give an equivalent definition of the generalized Kato spectrum.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Semilinear fractional order integro-differential inclusions with infinite delay
- Quasi-nilpotent perturbations of the generalized Kato spectrum
- Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
- Relations between BV*(q;α) and Λ*BVp classes of functions
- On the constancy of signs and order of magnitude of Fourier–Haar coefficients
- On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations
- Optimal control problem for the equation of vibrations of an elastic plate
- Generalized Hausdorff capacities and their applications
- Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
- A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field
- A note on the Borel types of some small sets
- On some boundary value problems for the heat equation in a non-regular type of a prism of ℝN+1
- Some weighted integral inequalities for differentiable h-preinvex functions
- Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
- On Baer invariants of pairs of groups
- The Arzelà–Ascoli theorem by means of ideal convergence
- Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV
Articles in the same Issue
- Frontmatter
- Semilinear fractional order integro-differential inclusions with infinite delay
- Quasi-nilpotent perturbations of the generalized Kato spectrum
- Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation
- Relations between BV*(q;α) and Λ*BVp classes of functions
- On the constancy of signs and order of magnitude of Fourier–Haar coefficients
- On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations
- Optimal control problem for the equation of vibrations of an elastic plate
- Generalized Hausdorff capacities and their applications
- Approximation by bivariate (p,q)-Baskakov–Kantorovich operators
- A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field
- A note on the Borel types of some small sets
- On some boundary value problems for the heat equation in a non-regular type of a prism of ℝN+1
- Some weighted integral inequalities for differentiable h-preinvex functions
- Computation of minimal homogeneous generating sets and minimal standard bases for ideals of free algebras
- On Baer invariants of pairs of groups
- The Arzelà–Ascoli theorem by means of ideal convergence
- Absolute convergence of multiple Fourier series of a function of p(n)-Λ-BV
