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Higher point derivations on commutative Banach algebras, II

Dales, H.G. and McClure, J. P. (1977) Higher point derivations on commutative Banach algebras, II. Journal of the London Mathematical Society, 16 (2). pp. 313-325. ISSN 0024-6107

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Abstract

This paper continues the study of continuity properties of higher point derivations on commutative Banach algebras. It is shown that there are uniform algebras and regular algebras which have totally discontinuous point derivations of infinite order. This shows that there can be no special automatic continuity results for higher point derivations either for uniform algebras or for regular algebras. It is also shown that there are Banach algebras which have homomorphisms onto the algebra of complex formal power series. An important element in the constructions is a topological version of the symmetric tensor algebra over a vector space. These algebras may be of independent interest; related objects have already been considered by other authors.

Item Type: Article
Journal or Publication Title: Journal of the London Mathematical Society
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 67723
Deposited By: ep_importer_pure
Deposited On: 26 Nov 2013 11:28
Refereed?: Yes
Published?: Published
Last Modified: 21 Sep 2017 00:42
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/67723

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