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Decomposability of Finite Rank Operators in Lie Ideals of Nest Algebras

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Abstract

A set of operators is said to be decomposable if each finite rank operator in it can be written as a sum of finitely many rank-1 operators in it. In this note, we establish a sufficient and necessary condition on the nest such that each closed Lie ideal in the associated nest algebra is decomposable.

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Chaoqun Chen & Fangyan Lu

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  1. Chaoqun Chen
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  2. Fangyan Lu
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Correspondence to Fangyan Lu.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11171244).

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Chen, C., Lu, F. Decomposability of Finite Rank Operators in Lie Ideals of Nest Algebras. Integr. Equ. Oper. Theory 81, 427–434 (2015). https://doi.org/10.1007/s00020-014-2171-8

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  • DOI: https://doi.org/10.1007/s00020-014-2171-8

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