Finite Sections of Band-dominated Operators with Almost Periodic Coefficients
Vladimir Rabinovich, Steffen Roch, Bernd Silbermann · Birkhäuser Basel eBooks · 2007
We consider the sequence of the finite sections R n AR n of a band-dominated operator A on l 2(ℤ) with almost periodic coefficients. Our main result says that if the compressions of A onto ℤ+ and ℤ− are invertible, then there is a distinguished subsequence of (R n AR n) which is stable. Moreover, this subsequence proves to be fractal, which allows us to establish the convergence in the Hausdorff metric of the singular values and pseudoeigenvalues of the finite section matrices.