Abstract
This paper is continuation of paper Ammar et al. (Mediterr J Math 12(4):1377–1395, 2015). It gives some new results related to the pseudospectra and the essential pseudospectra of linear relations. We start by studying the stability of these pseudospectra and some characterization.
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Abdmouleh, F., Ammar, A., Jeribi, A.: A characterization of the pseudo-Browder essential spectra of linear operators and application to a transport equation. J. Comput. Theor. Transp. 44(3), 141–153 (2015)
Abdmouleh, F., Alvarez, T., Jeribi, A.: On a characterization of the essential spectra of a linear relation. (2015, preprint)
Álvarez, T., Ammar, A., Jeribi, A.: On the essential spectra of some matrix of linear relations. Math. Methods Appl. Sci. 37, 620–644 (2013)
Álvarez, T., Cross, R.W., Wilcox, D.: Multivalued Fredholm type operators with abstract generalised inverses. J. Math. Anal. Appl. 261(1), 403–417 (2001)
Álvarez, T.: Linear relations on hereditarily indecomposable normed spaces. Bull. Aust. Math. Soc. 84(1), 49–52 (2011)
Álvarez, T.: On almost semi-Fredholm linear relations in normed spaces. Glasg. Math. J. 47(1), 187–193 (2005)
Ammar, A., Jeribi, A.: A characterization of the essential pseudospectra on a Banach space. J. Arab. Math. 2, 139–145 (2013)
Ammar, A., Jeribi, A.: A characterization of the essential pseudospectra and application to a transport equation. Extracta Math. 28, 95–112 (2013)
Ammar, A., Jeribi, A.: Measures of noncompactness and essential pseudospectra on Banach space. Math. Meth. Appl. Sci. 37, 447–452 (2014)
Ammar, A., Daoud, H., Jeribi, A.: Pseudospectra and essential pseudospectra of multivalued linear relations. Mediterr. J. Math. 12(4), 1377–1395 (2015)
Ammar, A., Boukettaya, B., Jeribi, A.: A note on the essential pseudospectra and application. Linear Multilinear Algebra (2015). doi:10.1080/03081087.2015.1091436
Cross, R.W.: Multivalued linear operators. Marcel Dekker, New York (1998)
Davies, E.B.: Linear operators and their spectra. United States of America by Cambridge University Press, New York (2007)
Hinrichsen, D., Pritchard, A.J.: Robust stability of linear operators on Banach spaces. J. Control Optim. 32, 1503–1541 (1994)
Jeribi, A.: Spectral theory and applications of linear operators and block operator matrices. Springer-Verlag, New York (2015)
Landau, H.J.: On Szego’s eigenvalue distribution theorem and non-Hermitian kernels. J. Analyse Math. 28, 335–357 (1975)
Trefethen, L.N.: Pseudospectra of matrices. In: Numerical analysis 1991 (Dundee, 1991), Pitman Res. Notes Math. Ser., vol. 260, pp. 234–266. Longman Sci. Tech., Harlow (1992)
Varah, J.M.: The computation of bounds for the invariant subspaces of a general matrix operator. Thesis (Ph.D.), Stanford University. ProQuest LLC, Ann Arbor (1967)
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Ammar, A., Daoud, H. & Jeribi, A. The stability of pseudospectra and essential pseudospectra of linear relations. J. Pseudo-Differ. Oper. Appl. 7, 473–491 (2016). https://doi.org/10.1007/s11868-016-0150-3
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DOI: https://doi.org/10.1007/s11868-016-0150-3