caa a22 4500 386385963 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S030500410000147X doi S030500410000147X pii (NATIONALLICENCE)cambridge-10.1017/S030500410000147X Hennings M. A. Sidney Sussex College, Cambridge, CB2 3HU Power-bounded elements and tauberian theorems in locally convex algebras [Elektronische Daten] [M. A. Hennings] The tauberian theorems concerning power-bounded elements of Banach algebras studied by Katznelson and Tzafriri, Allan, O'Farrell and Ransford and Allan are considered, and it is shown that (almost) exactly the same results are true for power-bounded elements in a very large class of locally convex topological algebras, the pseudo-complete algebras. The submultiplicativity of the Banach algebra norm is, for once, inessential to the proof of these theorems. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 147-159 0305-0041 105:1<147 1989 105 PSP https://doi.org/10.1017/S030500410000147X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030500410000147X text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hennings M. A. Sidney Sussex College, Cambridge, CB2 3HU NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 147-159 0305-0041 105:1<147 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge