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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Bibliographic Details
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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Summary: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.
ISSN:0011-4642
1572-9141
DOI:10.1007/s10587-016-0294-6