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1995 | 115 | 1 | 39-52
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Some results about Beurling algebras with applications to operator theory

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We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying $∥T^n∥ = O(n^β)$ as n → ∞ for some β ≥ 0, then $∑_{n=1}^∞ ∥(1-T)^n x∥/∥(1-T)^{n-1}x∥$ diverges for every x ∈ X such that $(1-T)^{[β]+1}x ≠ 0$.
Słowa kluczowe
  • Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge, CB2 1SB, England ,
  • Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700 South Africa
  • [1] A. Atzmon, Operators which are annihilated by analytic functions and invariant subspaces, Acta Math. 144 (1980), 27-63.
  • [2] C. Bennett and J. E. Gilbert, Homogeneous algebras on the circle: I. Ideals of analytic functions, Ann. Inst. Fourier (Grenoble) 22 (3) (1972), 1-19.
  • [3] J. G. Caughran, Factorization of analytic functions with $H^p$ derivative, Duke Math. J. 36 (1969), 153-158.
  • [4] J. Esterle et F. Zouakia, Rythme de décroissance des itérés de certains opérateurs de l'espace de Hilbert, J. Operator Theory 21 (1989), 387-396.
  • [5] I. M. Gelfand, D. A. Raikov and G. E. Shilov, Commutative Normed Rings, Chelsea, Bronx, 1964.
  • [6] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  • [7] J.-P. Kahane, Idéaux primaires fermés dans certaines algèbres de Banach de fonctions analytiques, in: E. J. Akutowicz (ed.), L'analyse harmonique dans le domaine complexe, Lecture Notes in Math. 336, Springer, Berlin, 1973, 5-14.
  • [8] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968.
  • [9] T. V. Pedersen, Norms of powers in Banach algebras, Bull. London Math. Soc., to appear.
  • [10] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford Univ. Press, London, 1968.
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