| Title:
|
On the defect spectrum of an extension of a Banach space operator (English) |
| Author:
|
Kordula, Vladimír |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
609-616 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T$ be an operator acting on a Banach space $X$. We show that between extensions of $T$ to some Banach space $Y\supset X$ which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum. (English) |
| MSC:
|
47A10 |
| MSC:
|
47A20 |
| idZBL:
|
Zbl 0954.47002 |
| idMR:
|
MR1658217 |
| . |
| Date available:
|
2009-09-24T10:16:32Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127441 |
| . |
| Reference:
|
[1] S. Axler, J. Conway, G. McDonald: Toeplitz operators on Bergman spaces.Canad. J. Math. 34 (1982), 466–483. MR 0658979, 10.4153/CJM-1982-031-1 |
| Reference:
|
[2] B. Bollobás: To what extent can the spectrum of an operator be diminished under an extension, in: Linear and Complex Analysis Problem Book, V. P. Havin, S. V. Hruščev and N. K. Nikol’skij (eds.), Lecture Notes in Math. 1043, Springer, Berlin 1984, 210.. |
| Reference:
|
[3] V. Müller: Adjoint inverses to noncommutative Banach algebras and extensions of operator.Studia Math. 91 (1988), 73–77. MR 0957286, 10.4064/sm-91-1-73-77 |
| Reference:
|
[4] V. Müller: On the joint essential spectrum of commuting operators.Acta Sci. Math. Szeged 57 (1993), 199–205. MR 1243277 |
| Reference:
|
[5] C. J. Read: Spectrum reducing extensions for one operator on a Banach space.Trans. Amer. Math. Soc. 308 (1988), 413–429. MR 0946450, 10.1090/S0002-9947-1988-0946450-5 |
| Reference:
|
[6] Z. Słodkovski and W. .Zelazko: On the joint spectra of commuting families of operators.Studia Math. 50 (1974), 127–148. MR 0346555, 10.4064/sm-50-2-127-148 |
| Reference:
|
[7] W. .Zelazko: On a problem concerning joint approximate point spectra.Studia Math. 45 (1973), 239–240. Zbl 0256.47002, MR 0336382, 10.4064/sm-45-3-239-240 |
| . |
