Abstract
Let T(a) be the infinite Toeplitz matrix with the symbol a and let T n (a) denote the n × n principal submatrix of T(a). The pseudospectra of T n (a) are known to converge to the pseudospectrum of T(a) as n → ∞ provided a is piecewise continuous. Only recently, Mark Embree, Nick Trefethen, and one of the authors observed that this convergence may be spectacularly slow in case a has a jump. The main result of this paper says that such a slow convergence of pseudospectra is generic even within the class of continuous symbols.
This author was partially supported by DAAD grant A/01/06411 and by CONACYT grant, Câ.tedra Patrimonial, Nivel II, No. 010286.
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To Georgii Semenovitch Litvinchuk on his 70th birthday
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Böttcher, A., Grudsky, S. (2003). Toeplitz Matrices with Slowly Growing Pseudospectra. In: Samko, S., Lebre, A., dos Santos, A.F. (eds) Factorization, Singular Operators and Related Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0227-0_4
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DOI: https://doi.org/10.1007/978-94-017-0227-0_4
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