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Growth conditions on powers of Hermitian elements

Published online by Cambridge University Press:  24 October 2008

K. J. Falconer
K. J. Falconer
Affiliation:
University of Bristol
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Extract

Roe (7) has recently given a striking characterization of the sine function as essentially the only function defined on the real line which has all its derivatives and successive ‘integrals’ bounded by a uniform bound, and this result has since been generalized by Burkill (5). In this note we relate this work to Banach algebra theory in a natural way by demonstrating the equivalence of Theorems 1 and 2 below, and also by giving a direct proof of Theorem 1. (Theorem 2 is Burkill's generalization of Roe's result stated in complex form.) We enunciate a Banach space version of the result (Theorem 3), and a further generalization of all these results is given in Theorem 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 115 - 119
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

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