Graded Banach algebras associated with varieties of Banach algebras

by P.G.Dixon

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 `algebraically defined'.)


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Expanded notes of a talk at Leeds based on this paper may be downloaded in .PDF format here.

Notes of a more general talk at Lancaster may be downloaded in .PDF format here.

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