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Seidel, Markus

On \((N,\epsilon)\)-pseudospectra of operators on Banach spaces. (English) Zbl 1307.47005

J. Funct. Anal. 262, No. 11, 4916-4927 (2012).
Summary: In this paper, we extend the concept of the \((N,\epsilon )\)-pseudospectra of A. C. Hansen [J. Funct. Anal. 254, No. 8, 2092–2126 (2008; Zbl 1138.47002); J. Am. Math. Soc. 24, No. 1, 81–124 (2011; Zbl 1210.47013)] to the case of bounded linear operators on Banach spaces and prove several relations to the usual spectrum. We particularly discuss the approximation by rectangular finite sections and the impact of the fundamental result of E. Shargorodsky [Bull. Lond. Math. Soc. 40, No. 3, 493–504 (2008; Zbl 1147.47007)] on “jumping” pseudospectra.

Cited in 14 Documents

MSC:

47A10 Spectrum, resolvent
47A58 Linear operator approximation theory
65J05 General theory of numerical analysis in abstract spaces

Keywords:

spectrum; pseudospectrum; Banach space; quasi-diagonal operator

Citations:

Zbl 1138.47002; Zbl 1210.47013; Zbl 1147.47007

Software:

Eigtool
Cite Review PDF
Full Text: DOI

References:

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