Journal of Operator Theory

Volume 77, Issue 1, Winter 2017  pp. 171-189.

Compact multiplication operators on nest algebras

Authors:  G. Andreolas (1) and M. Anoussis (2)
Author institution:(1) Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
(2) Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece

Summary: Let $\mathcal{N}$ be a nest on a Hilbert space $H$ and $\mathrm{Alg}\,\mathcal{N}$ 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 $\mathrm{Alg}\,\mathcal{N}$. We also show that there is no non-zero weakly compact multiplication operator on $\mathrm{Alg}\,\mathcal{N}/\mathrm{Alg}\,\mathcal{N}\cap \mathcal{K}(H)$.

DOI: http://dx.doi.org/10.7900/jot.2016mar10.2090
Keywords: nest algebra, compact multiplication operators, elementary operator, weakly compact, Calkin algebra, Jacobson radical