Geodesic
On commutative non-self-adjoint operator algebras
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 54-59

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Kelly, R. H. On commutative non-self-adjoint operator algebras. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 54-59. doi: 10.1017/S0017089500002111
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