Some results about Beurling algebras with applications to operator theory

• Autorzy: Thomas Vils Pedersen
• Języki publikacji: EN

Abstrakty

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 $(1-T)^{[β]+1}x ≠ 0$.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 47A30: Norms (inequalities, more than one norm, etc.)
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 115
• Numer: 1
• Strony: 39-52

Daty

wydano

1995

Twórcy

autor

Thomas Vils Pedersen

• 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

Bibliografia

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