Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra
| Autor: | Makai, Jr., E., Zemánek, Jaroslav |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pdf pages |
| Databáze: | arXiv |
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