COMPACT MULTIPLICATION OPERATORS ON NEST ALGEBRAS

Let N be a nest on a Hilbert space H and Alg N the corresponding nest algebra. We obtain a characterization of the compact and weakly compact multiplication operators defined on nest algebras. This characterization leads to a description of the closed ideal generated by the compact elements of Alg N...

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Published in:Journal of operator theory 2017, Vol.77 (1), p.171-189
Main Authors: ANDREOLAS, G., ANOUSSIS, M.
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description Let N be a nest on a Hilbert space H and Alg N the corresponding nest algebra. We obtain a characterization of the compact and weakly compact multiplication operators defined on nest algebras. This characterization leads to a description of the closed ideal generated by the compact elements of Alg N. We also show that there is no non-zero weakly compact multiplication operator on Alg N/Alg N ∩ K(H).
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