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Journal of the London Mathematical Society 1984 s2-29(1):171-174; doi:10.1112/jlms/s2-29.1.171
© 1984 by London Mathematical Society
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© Oxford University Press

Algebras Generated by a Contraction

Karim Seddighi

Department of Mathematics and Statistics, University of Calgary 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4

Received 10 November 1982.

For a bounded linear operator T defined on the Hilbert space H let A(T)(W(T)) denote the weakstar (WOT) closed algebra generated by T and the identity.

In their paper [2] S. Brown, B. Chevreau and C. Pearcy characterize the predual of A(T), where T is a contraction with rich spectrum. We shall generalize this result slightly and use a result of R. Olin and J. Thomson to show that for such a contraction A{T) = W(T).


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