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On the algebra generated by a Hermitian operator

Published online by Cambridge University Press:  20 January 2009

H. R. Dowson
H. R. Dowson
Affiliation:
University of Glasgowyy
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The purpose of this note is to solve a problem of Dr A. M. Sinclair. Denote by Aw(I, T) the algebra with identity generated by a bounded linear operator T in the weak operator topology. We prove the following result.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 2 , December 1972 , pp. 89 - 91
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Bade, W. G., On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345–359.CrossRefGoogle Scholar
(2) Berkson, E., A characterization of scalar type operators on reflexive Banach spaces, Pacific J. Math. 13 (1963), 365–373.CrossRefGoogle Scholar
(3) DieudonnÉ, J., Sur la bicommutante d'une algèbre d'opèrateurs, Portugal Math. 14 (1955), 35–38.Google Scholar
(4) Dowson, H. R., On some algebras of operators generated by a scalar-type spectral operator, J. London Math. Soc. 40 (1965), 589–593.CrossRefGoogle Scholar
(5) Halpertn, I., Function spaces, Canad. J. Math. 5 (1953), 273–288.CrossRefGoogle Scholar
(6) Lorentz, G., Some new functional spaces, Ann. of Math. (2) 51 (1950), 37–55.CrossRefGoogle Scholar
(7) Lorentz, G., On the theory of spaces A, Pacific J. Math. 1 (1951), 411–429.CrossRefGoogle Scholar