| Title:
|
Noninvertibility preservers on Banach algebras (English) |
| Author:
|
Kuzma, Bojan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
919-921 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that a linear surjection $\Phi \:\mathcal A\rightarrow \mathcal B$, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective. (English) |
| Keyword:
|
linear preserver |
| Keyword:
|
noninvertible element |
| Keyword:
|
semisimple Banach algebra |
| Keyword:
|
socle |
| MSC:
|
46H05 |
| MSC:
|
46H10 |
| MSC:
|
47B48 |
| MSC:
|
47B49 |
| idZBL:
|
Zbl 1164.46337 |
| idMR:
|
MR2261663 |
| . |
| Date available:
|
2009-09-24T11:39:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128116 |
| . |
| Reference:
|
[1] B. Aupetit: A Primer on Spectral Theory.Springer-Verlag, New York, 1991. Zbl 0715.46023, MR 1083349 |
| Reference:
|
[2] B. Aupetit, H. du T. Mouton: Spectrum-preserving linear mappings in Banach algebras.Stud. Math. 109 (1994), 91–100. MR 1267714, 10.4064/sm-109-1-91-100 |
| Reference:
|
[3] M. Brešar, A. Fošner, and P. Šemrl: A note on invertibility preservers on Banach algebras.Proc. Amer. Math. Soc. 131 (2003), 3833–3837. MR 1999931, 10.1090/S0002-9939-03-07192-2 |
| Reference:
|
[4] A. R. Sourour: Invertibility preserving maps on $L(X)$.Trans. Amer. Math. Soc. 348 (1996), 13–30. MR 1311919, 10.1090/S0002-9947-96-01428-6 |
| . |
