Displaying similar documents to “On the spectral set of a solvable Lie algebra of operators.”

Spectrum for a solvable Lie algebra of operators

Daniel Beltiţă (1999)

Studia Mathematica


A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.

Invariant subspaces and spectral mapping theorems

V. Shul'man (1994)

Banach Center Publications


We discuss some results and problems connected with estimation of spectra of operators (or elements of general Banach algebras) which are expressed as polynomials in several operators, noncommuting but satisfying weaker conditions of commutativity type (for example, generating a nilpotent Lie algebra). These results have applications in the theory of invariant subspaces; in fact, such applications were the motivation for consideration of spectral problems. More or less detailed proofs...

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.

Lie solvable groups algebras of derived length three.

Meena Sahai (1995)

Publicacions Matemàtiques


Let K be a field of characteristic p > 2 and let G be a group. Necessary and sufficient conditions are obtained so that the group algebra KG is strongly Lie solvable of derived length at most 3. It is also shown that these conditions are equivalent to KG Lie solvable of derived length 3 in characteristic p ≥ 7.

The classification of two step nilpotent complex Lie algebras of dimension 8

Zaili Yan, Shaoqiang Deng (2013)

Czechoslovak Mathematical Journal


A Lie algebra 𝔤 is called two step nilpotent if 𝔤 is not abelian and [ 𝔤 , 𝔤 ] lies in the center of 𝔤 . Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension...