Journal of Operator Theory

Volume 70, Issue 2, Autumn 2013 pp. 355-373.

Subideals of operators

Authors: Sasmita Patnaik (1) and Gary Weiss (2)
Author institution: (1) Department of Mathematics, University of Cincinnati, OH,45221-0025 , U.S.A.
(2) Department of Mathematics, University of Cincinnati, OH,45221-0025 , U.S.A.

Summary: A subideal is an ideal of an ideal of $B(H)$ and a principal subideal is a principal ideal of an ideal of $B(H)$. We determine necessary and sufficient conditions for a principal subideal to be an ideal of $B(H)$. This generalizes to arbitrary ideals the 1983 work of Fong and Radjavi characterizing principal subideals of the ideal of compact operators that are also ideals of $B(H)$. We then characterize all principal subideals. We also investigate the lattice structure of subideals as part of the general study of ideal lattices such as the often studied lattice structure of ideals of $B(H)$. This study of subideals and the study of elementary operators with coefficient constraints are closely related.

DOI: http://dx.doi.org/10.7900/jot.2011sep02.1926
Keywords: ideals, operator ideals, principal ideals, subideals, lattices

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