caa a22 4500 386385122 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198903 xx s 000 0 eng 10.1017/S0305004100067840 doi S0305004100067840 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100067840 Gourdeau Frédéric Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB Amenability of Banach algebras [Elektronische Daten] [Frédéric Gourdeau] We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1]. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 351-355 0305-0041 105:2<351 1989 105 PSP https://doi.org/10.1017/S0305004100067840 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100067840 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gourdeau Frédéric Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/2(1989-03), 351-355 0305-0041 105:2<351 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge