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arXiv · 2110.01569

On Simplicity of Lie Algebras of Compact Operators: A Direct Approach

Sasmita Patnaik
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Abstract

We investigate an algebraic variant of the Wojty\'nski problem on the simplicity of Lie algebras of compact operators on a separable infinite-dimensional complex Hilbert space. We prove the non-simplicity of Lie algebras of compact operators under a mild softness condition using the notion of soft-edged operator ideals introduced by Kaftal and Weiss. We believe our study offers a new perspective on the investigation of the simplicity of Lie algebras by relating it to the study of operator ideals.

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Sasmita Patnaik. 2021-10-04. On Simplicity of Lie Algebras of Compact Operators: A Direct Approach. https://arxiv.org/abs/2110.01569

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