Generalizations of Cesàro means and poles of the resolvent

• Autorzy: Laura Burlando
• Języki publikacji: EN

Abstrakty

EN

An improvement of the generalization-obtained in a previous article [Bu1] by the author-of the uniform ergodic theorem to poles of arbitrary order is derived. In order to answer two natural questions suggested by this result, two examples are also given. Namely, two bounded linear operators T and A are constructed such that $n^{-2}Tⁿ$ converges uniformly to zero, the sum of the range and the kernel of 1-T being closed, and $n^{-3} ∑_{k=0}^{n-1} A^{k}$ converges uniformly, the sum of the range of 1-A and the kernel of (1-A)² being closed. Nevertheless, 1 is a pole of the resolvent of neither T nor A.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 164
• Numer: 3
• Strony: 257-281

Daty

wydano

2004

Twórcy

autor

Laura Burlando

• Dipartimento di Matematica dell'Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy

Identyfikatory

DOI

10.4064/sm164-3-5