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

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, tha...

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Published in:Czechoslovak mathematical journal 2016-09, Vol.66 (3), p.821-828
Main Authors: Makai, Endre, Zemánek, Jaroslav
Format: Article
Language:English
Subjects:
Algebra
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
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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.
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subjects Algebra
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
title Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra
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