| Title:
|
On a certain class of subspectra (English) |
| Author:
|
Sołtysiak, Andrzej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
715-721 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting $n$-tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity. (English) |
| Keyword:
|
Banach algebra |
| Keyword:
|
joint spectrum |
| Keyword:
|
subspectrum |
| Keyword:
|
spectroid |
| Keyword:
|
geometrical spectral radius |
| Keyword:
|
(joint) capacity |
| MSC:
|
46H05 |
| MSC:
|
46H30 |
| MSC:
|
47A13 |
| idZBL:
|
Zbl 0763.46037 |
| idMR:
|
MR1159818 |
| . |
| Date available:
|
2009-01-08T17:48:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118451 |
| . |
| Reference:
|
[1] Chō M., Takaguchi M.: Boundary points of joint numerical ranges.Pacific J. Math. 95 (1981), 27-35. MR 0631656 |
| Reference:
|
[2] Chō M., Żelazko W.: On geometric spectral radius of commuting $n$-tuples of operators.to appear in Hokkaido Math. J. MR 1169792 |
| Reference:
|
[3] Słodkowski Z., Żelazko W.: A note on semicharacters.in: Banach Center Publications, vol. 8, Spectral Theory, PWN, Warsaw, 1982, 397-402. MR 0738305 |
| Reference:
|
[4] Sołtysiak A.: Capacity of finite systems of elements in Banach algebras.Comment. Math. 19 (1977), 381-387. MR 0477779 |
| Reference:
|
[5] Sołtysiak A.: Some remarks on the joint capacities in Banach algebras.ibid. 20 (1978), 197-204. MR 0463939 |
| Reference:
|
[6] Stirling D.S.G.: The joint capacity of elements of Banach algebras.J. London Math. Soc. (2), 10 (1975), 212-218. Zbl 0302.46035, MR 0370195 |
| Reference:
|
[7] Żelazko W.: An axiomatic approach to joint spectra I.Studia Math. 64 (1979), 249-261. MR 0544729 |
| Reference:
|
[8] Żelazko W.: Banach Algebras.Elsevier, PWN, Amsterdam, Warsaw, 1973. MR 0448079 |
| . |
