# 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

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