LOCAL ERGODIC PROPERTIES FOR POWERS OF OPERATORS IN BANACH SPACES

Dedicated to the memory of Professor Mihail Megan

Laurian Suciu^†

Abstract: In this paper we deal with the local convergence of a sequence {T_n} in the convex hull of the powers of an operator T on a Banach space X . We refer to the case when the sequence {T_n(T – I)} is bounded, and to the subspaces of X on which these two sequences converge to zero, respectively. Also, we study the behavior of f(T_nx) or f(T_n(T – I)x) for x ∈ X and f in the dual space X* of X, in particular when X is a Banach algebra and f a character of X. Some consequences concerning the Cesaro means of higher order are also derived.

Keywords: Cesaro mean, ergodicity, ascent of an operator.

MSC: 47A35, 47A10, 47A16.

DOI 10.56082/annalsarscimath.2026.3.129

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Accepted for publication on June 17, 2026
^†laurians2002@yahoo.com, Lucian Blaga University of Sibiu, Department of Mathematics and Informatics, Sibiu, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997