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Analytic joint spectral radius in a solvable Lie algebra of operators

100%
Beltiţă D.
Studia Mathematica
|
2001
|
tom 144
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nr 2
153-167
EN
We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.
2
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Spectrum for a solvable Lie algebra of operators

100%
Beltiţă D.
Studia Mathematica
|
1999
|
tom 135
|
nr 2
163-178
EN
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.
3
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On universal enveloping algebras in a topological setting

63%
Beltiţă D., Nicolae M.
Studia Mathematica
|
2015
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tom 230
|
nr 1
1-29
EN
We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups to pre-Lie groups. The latter class includes for instance all locally compact groups, Banach-Lie groups, additive groups underlying locally convex vector spaces, and also mapping groups consisting of rapidly decreasing Lie group-valued functions.
4
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Finite-dimensional Lie subalgebras of algebras with continuous inversion

63%
Beltiţă D., Neeb K.-H.
Studia Mathematica
|
2008
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tom 185
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nr 3
249-262
EN
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute modulo the Jacobson radical.
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