Various questions on Lie ideals of C∗-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators, nilpotents, and the range of polynomials; characterization of Lie ideals as similarity invariant subspaces.

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a complex symmetric operator. In fact, we prove that this property characterizes nilpotents of order two among all nonzero bounded operators. Second, we establish...

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Abstract In this paper, we introduce a generalization of G-opers for arbitrary parabolic subgroups P G complex semisimple Lie group. For associated to “even nilpotents”, parameterize ( , ) -opers by an object generalizing the base Hitchin fibration. particular, describe and families opers higher Teichmuller spaces.

Choose a random linear operator on vector space of finite cardinality N; then the probability that it is nilpotent 1/N. This analogue fact for self-map set N, some iterate constant The first result due to Fine, Herstein, and Hall, second essentially Cayley’s tree formula. We give new proof nilpotents, analogous Joyal’s beautiful It uses only general algebra avoids calculation entirely.