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An extreme point theorem for inverses in a Banach algebra with identity

Published online by Cambridge University Press:  24 October 2008

J. G. Stampfli
J. G. Stampfli
Affiliation:
New York University
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Extract

A version of Corollary 2 for Hilbert space was orally communicated to the author by C. Pearcy. His proof employed facts about the numerical range, inner products, and orthogonality, and thus made use of structure peculiar to Hilbert space. A Banach algebra with identity is a more comfortable setting for these results, and there it is much clearer just what is important in each proof.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 993 - 994
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bohnenblust, H. G. and Karlin, S.Geometric properties of the unit sphere of Banach algebras. Annals of Math. 62 (1955), 217–229.CrossRefGoogle Scholar
(2)Lumer, G.Semi-inner-product spaces. Trans. Amer. Math. Soc. 100 (1961), 29–43.CrossRefGoogle Scholar