Analytic joint spectral radius in a solvable Lie algebra of operators
Volume 144 / 2001
Studia Mathematica 144 (2001), 153-167
MSC: Primary 47A13; Secondary 17B30, 28B05.
DOI: 10.4064/sm144-2-4
Abstract
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.
