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.
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