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arXiv · 1601.01505

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

E. Makai, Jr.·Jaroslav Zemánek
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Abstract

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 will 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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BibTeXRIS

E. Makai, Jr., Jaroslav Zemánek. 2016-01-07. Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra. https://arxiv.org/abs/1601.01505

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