Graded Banach algebras associated with varieties of Banach algebras
to appear in Math. Proc. Cambridge Philos. Soc.
2000 Mathematics Subject Classification: 46H05; 16R10.
The concept of `varieties of Banach algebras' was introduced by the author
(Quart. J. Math. Oxford (2), 27 (1976), 481--487). Here we develop the theory, producing
analogues of the `relatively free' objects in varieties of universal algebras. We take as a test
question the problem of describing all varieties which are closed under bicontinuous isomorphisms
(i.e. varieties which are also semivarieties), and show that this may be answered easily with
the aid of these new concepts. (The answer is, as expected, just those varieties which are
Reprints of the paper available on request: e-mail P.Dixon with extension
@sheffield.ac.uk., or may be
downloaded in .PDF format (167Kb.) or zipped
Expanded notes of a talk at Leeds based on this paper may be downloaded in .PDF format
Notes of a more general talk at Lancaster may be downloaded in .PDF format here.
Other publications by P. G. Dixon. Return to P. G. Dixon home page