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• # Artykuł - szczegóły

## Studia Mathematica

2004 | 164 | 3 | 257-281

## Generalizations of Cesàro means and poles of the resolvent

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.

257-281

wydano
2004

### Twórcy

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