Makai, Endre and Zemánek, J. (2016) Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra. CZECHOSLOVAK MATHEMATICAL JOURNAL, 66 (3). pp. 821-828. ISSN 0011-4642
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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 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. © 2016, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SIMILARITY; POLYNOMIAL PATH; Polygonal path; distance of connected components; connected component of (self-adjoint) algebraic elements; centre of a Banach algebra; C*-algebra; Banach algebra; analytic path; (self-adjoint) idempotent; (local) pathwise connectedness |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 03 Jan 2017 18:09 |
| Last Modified: | 03 Jan 2017 18:09 |
| URI: | http://real.mtak.hu/id/eprint/44312 |
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