A characterization of the condition spectrum on Banach space

Aymen Ammar, Aref Jeribi, Kamel Mahfoudhi


The aim of this paper is to introduce new definition of spectrum of a linear operator called the condition pseudospectrum how has a nice spectral properties. One impetus for writing this paper is the issue of condition pseudospectrum introduced by Ransford in the journal of J. London Math. Soc. (1984). The latter study motivates us to investigate the condition pseudospectrum of linear operator on a Banach space. We begin by defining it and then we focus on the characterization, the stability and some properties of these spectra.

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E. B. Davies. Linear Operators and their spectra. Cambridge Studies in Advanced

Mathematics, 106. Camb. Univ. Press, Cambridge (2007).

A. Jeribi. Spectral theory and applications of linear operators and block operator

matrices. Springer-Verlag, New-York, (2015).

G. Karishna Kumar and S. H. Lui.Pseudospectrum and condition spectrum Operators

and Matrices. 1 , 121-145 (2015).

M. Karow. Eigenvalue condition numbers and a formula of Burke, Lewis and Overton.

Electron. J. Linear Algebra 15 (2006), 143-153.

S. H. Kulkarni and D. Sukumar. The condition spectrum. Acta Sci. Math. (Szeged)

, 3-4 , 625-641 (2008).

T. J. Ransford. Generalised spectra and analytic multivalued functions. J. London

Math. Soc. (2) 29 , no. 2, 306- 322 (1984).

M. Schechter. Principles of functional analysis. Second edition. Graduate Studies in

Mathematics, American Mathematical Society, Providence, RI, 36. (2002).

L. N. Trefethen.Pseudospectra of linear operators. SAIM rev. 39 (3) 383-406, (1997).

L. N. Trefethen and M. Embree.Spectra and pseudospectra: The behavior of

nonnormal matrices and operators. Prin. Univ. Press, Princeton and Oxford, (2005).

J. M. Varah. The computation of bounds for the invariant subspaces of a general

matrix operator. Ph.D. thesis, stanford university ProQuest LLC, Ann Arbor (1967).


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