Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Title:

Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Creator:

Makai Jr., Endre and Jaroslav Zemánek

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1a319b9c-05e6-4ecc-861f-ac581581d87d
uuid:1a319b9c-05e6-4ecc-861f-ac581581d87d
issn:0011-4642

Subject:

matematika, mathematics, Banach algebra, C*-algebra, (self-adjoint) idempotent, (local) pathwise connectedness, connected component of (self-adjoint) algebraic elements, similarity, analytic path, polynomial path, polygonal path, centre of a Banach algebra, distance of connected components, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C*-algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C*-algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the given equation. We also formulate open questions., Endre Makai Jr., Jaroslav Zemánek., and Obsahuje seznam literatury

Language:

English

Rights:

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

Coverage:

821-828

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false