Band-dominated operators on \(l^p\)-spaces: Fredholm indices and finite sections. (English) Zbl 1087.47013
The present paper deals with band-dominated operators on \(l^p(\mathbb Z)\), \(1<p<\infty \). It is proved that a band operator which is Fredholm on \(l^p(\mathbb Z)\) is also Fredholm on \(l^q(\mathbb Z)\) for all \(1<q< \infty\), and the index is independent of \(q\). Some generalizations for band-dominated operators are given. The index formula for band-dominated operators in terms of local indices of their limit operators is derived. This formula is applied to verify the stability of the finite section method for invertible band-dominated operators with slowly oscillating coefficients.
Reviewer: Dagmar Medková (Praha)
MSC:
47A53 | (Semi-) Fredholm operators; index theories |
65J10 | Numerical solutions to equations with linear operators |
47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
47L80 | Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) |