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arXiv · 0801.4862

On algebras generated by inner derivations

Tatiana Shulman·Victor Shulman
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Abstract

We look for an effective description of the algebra D_{Lie}(X,B) of operators on a bimodule X over an algebra B, generated by inner derivations. It is shown that in some important examples D_{Lie}(X,B) consists of all elementary operators x\to \sum_i a_ixb_i satisfying the conditions $\sum_i a_ib_i = \sum_i b_ia_i = 0. The Banach algebraic versions of these results are also obtained and applied to the description of closed Lie ideals in some Banach algebras, and to the proof of a density theorem for Lie algebras of operators on Hilbert space.

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Tatiana Shulman, Victor Shulman. 2008-07-17. On algebras generated by inner derivations. https://arxiv.org/abs/0801.4862

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