Spectral conditions on Lie and Jordan algebras of compact operators

Details Spectral conditions on Lie and Jordan algebras of compact operators Spectral conditions on Lie and Jordan algebras of compact operators

2008-03-31

arxiv.org/abs/0803.4361v1

J. Funct. Anal. 256 (2009), no. 10, 3143-3157

Mathematics

Operator Algebras

14 pages

Scientific paper

We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these conditions imply that the algebra is (simultaneously) triangularizable.

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