Power-bounded operators and related norm estimates

Journal of the London Mathematical Society

Volumn 70, Issue 2, 2004, Pages 463-478

  Kalton, N ^a   Montgomery Smith, S ^a   Oleszkiewicz, K ^c   Tomilov, Y ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b NICOLAUS COPERNICUS UNIVERSITY   (Poland)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7544245904     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610704005514     Document Type: Article

References (30)

1. N. ASMAR, Applied complex analysis with partial differential equations (Prentice Hall, 2002).
2. N.-E. BENAMARA and N. NIKOLSKI, 'Resolvent tests for similarity to a normal operator', Proc. London Math. Soc. 78 (1999) 585-626.
3. M. BERKANI, 'Inégalités et propriétés spectrales dans les algèbres de Banach', PhD Thesis, Université de Bordeaux, 1983.
4. M. BERKANI, J. ESTERLE and A. MOKHTARI, 'Distance entre puissances d'une unité approchée bornée', J. London Math. Soc. 67 (2003) 1-20.
5. p-spaces', J. Funct. Anal. 183 (2001) 211-230.
6. S. BLUNCK, 'Maximal regularity of discrete and continuous time evolution equations', Studia Math. 146 (2001) 157-176.
7. F. F. BONSALL and M. J. CRABB, 'The spectral radius of a Hermitian element of a Banach algebra', Bull. London Math. Soc. 2 (1970) 178-180.
8. N. BOROVYKH, D. DRISSI and M. N. SPIJKER, 'A note about Ritt's condition, related resolvent conditions and power bounded operators', Numer. Funct. Anal. Optim. 21 (2000) 425-438.
9. nth powers lie close to the identity', Proc. Amer. Math. Soc. 23 (1969) 386-387.
10. R. M. CORLESS, G. H. GONNET, D. E. G. HARE, D. J. JEFFREY and D. E. KNUTH, 'On the Lambert W function', Adv. Comput. Math. 5 (1996) 329-359.
11. T. COULHON and L. SALOFF-COSTE, 'Puissances d'un opérateur régularisant', Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 419-436.
12. O. EL-FALLAH and T. J. RANSFORD, 'Extremal growth of powers of operators satisfying resolvent conditions of Kreiss-Ritt type', J. Funct. Anal., to appear.
13. ∞, and the closed ideal problem for commutative Banach algebras', Radical Banach Algebras and Automatic Continuity (Long Beach, CA, 1981), Lecture Notes in Mathematics 975 (Springer, Berlin, 1983) 66-162.
14. J. ESTERLE and A. MOKHTARI, 'Distance entre éléments d'un semi-groupe dans une algèbre de Banach', J. Funct. Anal. 195 (2002) 167-189.
15. E. A. GORIN, 'Several remarks in connection with Gelfand's theorems on the group of invertible elements of a Banach algebra', Funkcional. Anal. i Priložen. 12 (1978) 70-71 (Russian).
16. Y. KATZNELSON and L. TZAFRIRI, 'On power bounded operators', J. Funct. Anal. 68 (1986) 313-328.
17. M. G. KREIN, M. A. KRASNOSELSKII and D. P. MILMAN, 'On the defect numbers of linear operators in a Banach space and on some geometric properties', Sb. Trud. Inst. Matem. Akad. Nauk Ukr. SSR II (1948) 97-112.
18. J. LINDENSTRAUSS and L. TZAFRIRI, Classical Banach spaces. Vol. I: Sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete 92 (Springer, Berlin, 1977).
19. YU. LYUBICH, 'Spectral localization, power boundedness and invariant subspaces under Ritt's type condition', Studia Math. 134 (1999) 153-167.
20. YU. LYUBICH, 'The single-point spectrum operators satisfying Ritt's resolvent condition', Studia Math. 145 (2001) 135-142.
21. V. D. MILMAN and G. SCHECHTMAN, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics 1200 (Springer, Berlin, 1986).
22. B. NAGY and J. A. ZEMÁNEK, 'A resolvent condition implying power boundedness', Studia Math. 134 (1999) 143-151.
23. O. NEVANLINNA, Convergence of iterations for linear equations, Lectures in Mathematics, ETH Zürich (Birkhäuser, Basel, 1993).
24. O. NEVANLINNA, 'Resolvent conditions and powers of operators', Studia Math. 145 (2001) 113-134.
25. 2,, Studia, Math. 54 (1975) 149-159.
26. A. PEŁCZYŃSKI, 'All separable Banach spaces admit for every ε > 0 fundamental total and bounded by 1 + ε biorthogonal sequences', Studia Math. 55 (1976) 295-304.
27. n = 0', Proc. Amer. Math. Soc. 4 (1953) 898-899.
28. A. M. SINCLAIR, 'The norm of a hermitian element in a Banach algebra'. Proc. Amer. Math. Soc. 28 (1971) 446-450.
29. I. SINGER, Best approximation in normed linear spaces by elements of linear subspaces (Springer, Berlin, 1970).
30. Y. TOMILOV and J. ZEMÁNEK, 'A new way of constructing examples in operator ergodic theory', Math. Proc. Cambridge Philos. Soc., to appear.