ON THE UNIFORM ERGODIC THEOREM AND THE SP ECTRUM

Authors
MBEKHTA M ZEMANEK J
Citation
M. Mbekhta et J. Zemanek, ON THE UNIFORM ERGODIC THEOREM AND THE SP ECTRUM, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 317(12), 1993, pp. 1155-1158
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
317
Issue
12
Year of publication
1993
Pages
1155 - 1158
Database
ISI
SICI code
0764-4442(1993)317:12<1155:OTUETA>2.0.ZU;2-F
Abstract
The sequence of the arithmetic means of the powers of an operator T on a Banach space X converges in the operator norm if and only if n(-1)T (n) converges to zero as n --> + infinity and the range (I-T)(m)X is c losed for a certain m=1, 2,.... For the Riesz operators, other equival ent conditions are obtained. Also a theorem of Gelfand-Hille type is g iven in terms of the operator means.