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On commutative non-self-adjoint operator algebras

Published online by Cambridge University Press:  18 May 2009

R. H. Kelly
R. H. Kelly
Affiliation:
University of Glasgow, Glasgow G12 8QQ
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A proof is given here of a theorem of Sarason [9, Theorem 2], the proof being valid in an arbitrary (non-separable) complex Hilbert space. Sarason's proof uses a theorem and lemma of Wermer which may both fail when the separability hypothesis is omitted [3]. By using a special case of Sarason's theorem and another result of Sarason [10, Lemma 1] a simplified and shortened proof is given of a result of Scroggs [11, Corollary 1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 1 , March 1974 , pp. 54 - 59
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

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