Finite Sections of Band-Dominated Operators.
- 1st ed.
- 1 online resource (104 pages)
- Memoirs of the American Mathematical Society ; v.191 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- Chapter 1. Introduction: Band-dominated operators -- Chapter 2. Stability -- 2.1. Fredholm band-dominated operators and their indices -- 2.2. Algebras of matrix sequences -- 2.3. Stability vs. Fredholmness -- 2.4. Stability of the finite sections method -- 2.5. Band-dominated operators with slowly oscillating coefficients -- 2.6. The role of the index -- 2.7. The C*-algebra of the finite sections method -- 2.8. Another perspective on localization -- Chapter 3. Stable regularizability -- 3.1. Moore-Penrose invertibility in C*-algebras -- 3.2. Stable regularizability vs. Moore- Penrose invertibility -- 3.3. Stable regularizability of the finite sections method -- Chapter 4. Compactness -- 4.1. Compact sequences -- 4.2. Characterization via singular values -- 4.3. Central rank characterizations -- 4.4. Minimal and maximal characterizations -- 4.5. Compact sequences in S(N) and S(Z) -- Chapter 5. Fredholmness -- 5.1. Fredholm sequences -- 5.2. Fredholmness and stability -- 5.3. Fredholmness and stable regularizability -- 5.4. Fredholmness of the finite sections method -- 5.5. Slowly oscillating coefficients -- Chapter 6. Essential fractality -- 6.1. Fractality of quotient maps -- 6.2. J-fractal algebras -- 6.3. Essential fractality and singular values -- 6.4. Essential fractality of the finite sections algebras -- Chapter 7. Applications -- 7.1. Approximation numbers -- 7.2. Rank-preserving discretizations -- 7.3. Arveson dichotomy: band- dominated operators -- 7.4. Arveson dichotomy: the general setting -- 7.5. Essential spectra -- 7.6. Essential pseudospectra -- 7.7. Pseudomodes -- 7.8. Determinants -- Bibliography -- Index.