1. Subsets of nonempty joint spectrum in topological algebras
- Creator:
- Wawrzyńczyk, Antoni
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- joint spectrum, Waelbroeck algebra, commutator, and spectral mapping formula
- Language:
- English
- Description:
- We give a necessary and a sufficient condition for a subset S of a locally convex Waelbroeck algebra A to have a non-void left joint spectrum σl (S). In particular, for a Lie subalgebra L ⊂ A we have σl (L) ≠ ∅ if and only if [L, L] generates in A a proper left ideal. We also obtain a version of the spectral mapping formula for a modified left joint spectrum. Analogous theorems for the right joint spectrum and the Harte spectrum are also valid.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public