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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-4,
author = {Daniel Belti\c t\u a},
title = {Analytic joint spectral radius in a solvable Lie algebra of operators},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {153-167},
zbl = {0974.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-4}
}
Daniel Beltiţă. Analytic joint spectral radius in a solvable Lie algebra of operators. Studia Mathematica, Tome 147 (2001) pp. 153-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-4/