A note on the mapping theorem of essential pseudospectra on a Banach space
Abstract
UDC 517.98
The main goal of the paper is to determine some basic properties of the essential pseudospectrum of a bounded linear operator $A$ defined on a Banach space $X.$ We also prove two different versions of the essential pseudospectral mapping theorem.
References
A. Ammar, A. Jeribi, A characterization of the essential pseudospectra on a Banach space, Arab J. Math., 2, № 2, 139–145 (2013). DOI: https://doi.org/10.1007/s40065-012-0065-7
A. Ammar, A. Jeribi, A characterization of the essential pseudospectra and application to a transport equation, Extracta Math., 28, № 1, 95–112 (2013).
B. Gramsch, D. Lay, Spectral mapping theorems for essential spectra, Math. Ann., 192, 17–32 (1971). DOI: https://doi.org/10.1007/BF02052728
E. B. Davies, Linear operators and their spectra, Cambridge Stud. Adv. Math., 106, Cambridge Univ. Press, Cambridge (2007).
A. Jeribi, Spectral theory and applications of linear operators and block operator matrices, Springer, Cham (2015). DOI: https://doi.org/10.1007/978-3-319-17566-9
A. Jeribi, Linear operators and their essential pseudospectra, CRC Press (2018). DOI: https://doi.org/10.1201/9781351046275
N. Trefethen, M. Embree, Spectra and pseudospectra. The behavior of nonnormal matrices and operators, Princeton Univ. Press, Princeton, NJ (2005). DOI: https://doi.org/10.1515/9780691213101
S.-H. Lui, A pseudospectral mapping theorem, Math. Comp., 72, № 244, 1841–1854 (2003). DOI: https://doi.org/10.1090/S0025-5718-03-01542-4
R. Coleman, Calculus on normed vector spaces, Universitext, Springer, New York (2012). DOI: https://doi.org/10.1007/978-1-4614-3894-6
J. B. Conway, John course in functional analysis, Grad. Texts Math., 96, Springer-Verlag, New York (1985).
S.~H. Kulkarni, D.~Sukumar, The condition spectrum, Acta Sci. Math. (Szeged), 74, № 3-4, 625–641 (2008).
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