 | Chandler-Wilde S.N. Limit operators, collective compactness, and the spectral theory of infinite matrices / S.N.Chandler-Wilde, M.Lindner. - Providence: American Mathematical Society, 2011. - vii, 111 p.: ill. - (Memoirs of the American Mathematical Society; Vol.210, N 989). - Bibliogr.: p.103-107. - Ind.: p.111. - ISBN 978-0-8218-5243-9; ISSN 0065-9266
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Chapter 1. Introduction ......................................... 1
1.1. Overview ................................................... 1
1.2. A Brief History ............................................ 5
1.3. Summary and the Main New Results .......................... 16
Chapter 2. The Strict Topology ................................. 21
Chapter 3. Classes of Operators ................................ 29
3.1. Compactness and Collective Compactness on (Y, s) .......... 34
3.2. Algebraic Properties ...................................... 37
Chapter 4. Notions of Operator Convergence ..................... 41
Chapter 5. Key Concepts and Results ............................ 47
5.1. Invertibility at Infinity and Fredholmness ................ 47
5.2. A Generalised Collectively Compact Operator Theory ........ 48
5.3. Limit Operators ........................................... 50
5.4. Collective Compactness and the Operator Spectrum .......... 54
Chapter 6. Operators on ℓ P( N, U) .............................. 59
6.1. Periodic and Almost Periodic Operators .................... 60
6.2. Dual Space Arguments ...................................... 64
6.3. Band-Dominated Operators .................................. 68
6.4. Almost Periodic Band-Dominated Operators .................. 76
6.5. The Wiener Algebra ........................................ 82
Chapter 7. Discrete Schrödinger Operators ...................... 89
Chapter 8. A Class of Integral Operators ....................... 97
Chapter 9. Some Open Problems ................................. 101
Bibliography .................................................. 103
Index ......................................................... 109
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