03433nam 2200565 450 991081243860332120170822144127.01-4704-0501-6(CKB)3360000000465079(EBL)3114125(SSID)ssj0000888933(PQKBManifestationID)11480049(PQKBTitleCode)TC0000888933(PQKBWorkID)10875127(PQKB)11700887(MiAaPQ)EBC3114125(RPAM)15004273(PPN)195417844(EXLCZ)99336000000046507920070912h20082008 uy| 0engur|n|---|||||txtccrFinite sections of band-dominated operators /Steffen RochProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (104 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 895"Volume 191, number 895 (end of volume)."0-8218-4042-8 Includes bibliographical references (pages 83-85) and index.""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""Memoirs of the American Mathematical Society ;no. 895.Operator algebrasOperator theoryOperator algebras.Operator theory.512/.55Roch Steffen1958-60790MiAaPQMiAaPQMiAaPQBOOK9910812438603321Finite sections of band-dominated operators4110274UNINA