Premium
Higher Point Derivations on Commutative Banach Algebras, II
Author(s) -
Dales H. G.,
McClure J. P.
Publication year - 1977
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-16.2.313
Subject(s) - mathematics , commutative property , homomorphism , pure mathematics , tensor algebra , nest algebra , interior algebra , point (geometry) , banach algebra , algebra over a field , division algebra , algebra representation , non associative algebra , banach space , geometry
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.