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Quasispectra of solvable Lie algebra homomorphisms into Banach algebras

Anar Dosiev (2006)

Studia Mathematica

We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.

Quotients of L1 by reflexive subspaces.

Manuel González, Antonio Martínez-Abejón (1997)

Extracta Mathematicae

Here we present and example and some results suggesting that there is no infinite-dimensional reflexive subspace Z of L1 ≡ L1[0,1] such that the quotient L1/Z is isomorphic to a subspace of L1.

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