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Corrigenda

Published online by Cambridge University Press:  24 October 2008

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Volume 92 (1982), 115–119

K. J. Falconer

School of Mathematics, University of Bristol

‘Growth conditions on powers of Hermitian elements’

The above paper aimed to obtain Banach algebra equivalents of the elegant theorems of Roe [2] and Burkill [1] which gave characterizations of the sine function. Professor John Duncan has kindly pointed out that the paper contains two oversights, with the result that the theorems stated are not the strict Banach algebra equivalents as was claimed. (The assertion on p. 117 that T is Hermitian is false if μ > 0, and at the bottom of p. 117 it follows from Theorem 2 that F0(t) = c1eit + c2eit so that a2 – e = 0.) Whilst Theorems 1–3 are correct as stated, the conclusions of Theorems 1 and 3 must be strengthened to provide equivalent versions when μ > 0. In the basic case when μ = 0, the analysis remains as given.

Type
Corrigenda
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 3 , May 1984 , pp. 513 - 515
Copyright
Copyright © Cambridge Philosophical Society 1984

References

REFERENCES

[1]Burkill, H.. Sequences characterizing the sine function. Math. Proc. Cambridge Philos. Soc. 89 (1981), 71–77.CrossRefGoogle Scholar
[2]Roe, J.. A characterization of the sine function. Math. Proc. Cambridge Philos. Soc. 87 (1980), 69–73.CrossRefGoogle Scholar
[3]Istrǎt̹escu, V. I.. Some remarks on Hermitian operators. Math. Sem. Notes Kobe Univ. 6. (1978), 47–50.Google Scholar