DOIAbstract
AbstractThe spectral value set spεB,CA of a bounded linear operator A on l2 is the union of the spectra of all operators of the form A+BKC, where ∥K∥<ε and B,C are fixed bounded linear operators. It turns out that small changes of ε may cause drastic changes of the set spεB,CA. We conjecture that this can never happen if B or C is compact and A is given by an infinite Toeplitz band matrix. In the present paper, this conjecture is proved for certain interesting operators B and C and for several classes of Toeplitz band matrices, including Hessenberg matrices and matrices of small bandwidth. Our approach is based on working with the monodromy group of the Riemann surface associated with the generating function of the matrix
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