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Trace-Class and Centralizers of an H*-Algebra

Parfeny P. Saworotnow
Proceedings of the American Mathematical Society
Vol. 26, No. 1 (Sep., 1970), pp. 101-104
DOI: 10.2307/2036811
Stable URL: http://www.jstor.org/stable/2036811
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Trace-Class and Centralizers of an H*-Algebra
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Abstract

Let A be a proper H*-algebra. Let τ(A) = {xy|x, y ∈ A}, let R(A) be the set of all bounded linear operators S on A such that S(xy) = (Sx)y for all x, y ∈ A and let C(A) be the closed subspace of R(A) generated by the operators of the form La:x → ax, a ∈ A. It is shown that τ(A) can be identified with the space of all bounded linear functionals on C(A) and that R(A) is the dual of τ(A). Also it is proved that τ(A) is a Banach algebra.

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