Dosiev, AnarMathematics2024-07-052024-07-0520060039-322310.4064/sm174-1-22-s2.0-33748798886https://doi.org/10.4064/sm174-1-2https://hdl.handle.net/20.500.14411/1177We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism pi of a finite-dimensional solvable Lie algebra g in terms of quasispectra sigma(pi). 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.eninfo:eu-repo/semantics/openAccessquasispectrasolvable Lie algebrafunctional calculusjoint spectral radiusArticleQ317411327WOS:0002406908000027