Can spectral value sets of Toeplitz band matrices jump? (Q1611898)

The authors study the limit behavior of the spectral value set \(sp_\varepsilon^{B,C} (A)=\bigcup_{\|K\|<\varepsilon} sp (A+BKC)\). Here \(B\) and \(C\) are fixed bounded linear operators. In the case \(B=C=I\) this spectral value set is called a pseudospectra. They consider the case when \(A\) is an infinite Toeplitz band matrix and study when \(sp_\varepsilon^{B,C} (A)\) cannot have a jump. The example when \(sp_\varepsilon^{B,C} (A)\) can jump is also given.