caa a22 4500 388046996 CHVBK 20180307125041.0 cr unu---uuuuu 161130e199804 xx s 000 0 eng 10.1017/S1446788700001749 doi S1446788700001749 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001749 Ergodicity and differences of functions on semigroups [Elektronische Daten] Iseki [11] defined a general notion of ergodicity suitable for functions : J → X where J is an arbitrary abelian semigroup and X is a Banach space. In this paper we develop the theory of such functions, showing in particular that it fits the general framework established by Eberlein [9] for ergodicity of semigroups of operators acting on X. Moreover, let A be a translation invariant closed subspace of the space of all bounded functions from J to X. We prove that if A contains the constant functions and is an ergodic function whose differences lie in A then A. This result has applications to spaces of sequences facilitating new proofs of theorems of Gelfand and Katznelson-Tzafriri [12]. We also obtain a decomposition for the space of ergodic vectors of a representation T: J → L(X) generalizing results known for the case J = Z+. Finally, when J is a subsemigroup of a locally compact abelian group G, we compare the Iseki integrals with the better known Cesàro integrals. Copyright © Australian Mathematical Society 1998 primary 43A60 nationallicence secondary 47A10 nationallicence 47D03 nationallicence 28B05 nationallicence Ergodic nationallicence semigroup nationallicence differences nationallicence Beurling spectrum nationallicence invariant means nationallicence system of invariant integrals nationallicence Basit Bolis Department of Mathematics Monash University Clayton, VIC 3168 Australia e-mail Pryde A. J. Department of Mathematics Monash University Clayton, VIC 3168 Australia e-mail: bbasit(ajpryde)@vaxc.cc.monash.edu.au Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 253-265 1446-7887 64:2<253 1998 64 JAZ https://doi.org/10.1017/S1446788700001749 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001749 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Basit Bolis Department of Mathematics Monash University Clayton, VIC 3168 Australia e-mail NATIONALLICENCE 700 1- Pryde A. J. Department of Mathematics Monash University Clayton, VIC 3168 Australia e-mail: bbasit(ajpryde)@vaxc.cc.monash.edu.au NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 253-265 1446-7887 64:2<253 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge