| Title:
|
Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra (English) |
| Author:
|
Makai, Endre Jr. |
| Author:
|
Zemánek, Jaroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
821-828 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Banach algebra |
| Keyword:
|
$C^*$-algebra |
| Keyword:
|
(self-adjoint) idempotent |
| Keyword:
|
connected component of (self-adjoint) algebraic elements |
| Keyword:
|
(local) pathwise connectedness |
| Keyword:
|
similarity |
| Keyword:
|
analytic path |
| Keyword:
|
polynomial path |
| Keyword:
|
polygonal path |
| Keyword:
|
centre of a Banach algebra |
| Keyword:
|
distance of connected components |
| MSC:
|
46H20 |
| MSC:
|
46L05 |
| idZBL:
|
Zbl 06644035 |
| idMR:
|
MR3556869 |
| DOI:
|
10.1007/s10587-016-0294-6 |
| . |
| Date available:
|
2016-10-01T15:26:10Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145873 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Kovarik, Z. V.: Similarity and interpolation between projectors.Acta Sci. Math. 39 (1977), 341-351. Zbl 0392.47008, MR 0482324 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] E. Makai, Jr., J. Zemánek: On the structure of the set of elements in a Banach algebra which satisfy a given polynomial equation, and their liftings. Available at www.renyi.mta.hu/ {makai}.. |
| Reference:
|
[8] E. Makai, Jr., J. Zemánek: On polynomial connections between projections.Linear Algebra Appl. 126 (1989), 91-94. Zbl 0714.47011, MR 1040774 |
| Reference:
|
[9] Trémon, M.: On the degree of polynomials connecting two idempotents of a Banach algebra.Proc. R. Ir. Acad. Sect. A 95 (1995), 233-235. Zbl 0853.46044, MR 1660382 |
| Reference:
|
[10] Tremon, M.: Polynômes de degré minimum connectant deux projections dans une algèbre de Banach.Linear Algebra Appl. French 64 (1985), 115-132. Zbl 0617.46054, MR 0776520 |
| Reference:
|
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| . |
