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Banach algebras of power series

Published online by Cambridge University Press:  09 April 2009

Richard J. Loy
Richard J. Loy
Affiliation:
School of General Studies, Australian National University, Canberra
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Let C[[t]] denote the algebra of all formal power series over the complex field C in a commutative indeterminate t with the weak topology determined by the projections pj: Σαiti ↦αj. A subalgebra A of C[[t]] is a Banach algebra of power series if it contains the polynomials and is a Banach algebra under a norm such that the inclusion map A ⊂ C[[t]] is continuous. Such algebras were first introduced in [13] when considering algebras with one generator, and studied, in a special case, in [23]. For a partial bibliography of their subsequent study and application see the references of [9] (note that the usage of the term Banach algebra of power series in [9] differs from that here), and also [2], [3], [11]. Indeed, an examination of their use in [11], under more general topological conditions than here, led the present author to the results of [14], [15], [16], [17].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 3 , May 1974 , pp. 263 - 273
Copyright
Copyright © Australian Mathematical Society 1974

References

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