Subsets of nonempty joint spectrum in topological algebras

Title:

Subsets of nonempty joint spectrum in topological algebras

Creator:

Wawrzyńczyk, Antoni

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a61ed8b2-18c5-43f7-b95a-41fb0a4b69b5
uuid:a61ed8b2-18c5-43f7-b95a-41fb0a4b69b5
doi:10.21136/MB.2018.0098-17

Subject:

joint spectrum, Waelbroeck algebra, commutator, and spectral mapping formula

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

441-448

Source:

Mathematica bohemica | 2018 Volume:143 | Number:4

Harvested from:

CDK

Metadata only:

false