| Title:
|
Some equivalent metrics for bounded normal operators (English) |
| Author:
|
Jabbarzadeh, Mohammad Reza |
| Author:
|
Hajipouri, Rana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
201-212 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some stronger and equivalent metrics are defined on $\mathcal {M}$, the set of all bounded normal operators on a Hilbert space $H$ and then some topological properties of $\mathcal {M}$ are investigated. (English) |
| Keyword:
|
Hilbert space |
| Keyword:
|
normal operator |
| Keyword:
|
equivalent metrics |
| Keyword:
|
composition operator |
| MSC:
|
47A05 |
| idZBL:
|
Zbl 06890415 |
| idMR:
|
MR3831487 |
| DOI:
|
10.21136/MB.2017.0101-16 |
| . |
| Date available:
|
2018-06-11T11:03:14Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147245 |
| . |
| Reference:
|
[1] Benharrat, M., Messirdi, B.: Strong metrizability for closed operators and the semi-Fredholm operators between two Hilbert spaces.Int. J. Anal. Appl. 8 (2015), 110-122. |
| Reference:
|
[2] Cordes, H. O., Labrousse, J. P.: The invariance of the index in the metric space of closed operators.J. Math. Mech. 12 (1963), 693-719. Zbl 0148.12402, MR 0162142 |
| Reference:
|
[3] Gilfeather, F.: Norm conditions on resolvents of similarities of Hilbert space operators and applications to direct sums and integrals of operators.Proc. Am. Math. Soc. 68 (1978), 44-48. Zbl 0381.47003, MR 0475583, 10.2307/2040905 |
| Reference:
|
[4] Kato, T.: Perturbation Theory for Linear Operators.Grundlehren der mathematischen Wissenschaften 132. Springer, Berlin (1976). Zbl 0342.47009, MR 0407617, 10.1007/978-3-642-66282-9 |
| Reference:
|
[5] Kaufman, W. E.: A stronger metric for closed operators in Hilbert space.Proc. Am. Math. Soc. 90 (1984), 83-87. Zbl 0551.47001, MR 0722420, 10.2307/2044673 |
| Reference:
|
[6] Kittaneh, F.: On some equivalent metrics for bounded operators on Hilbert space.Proc. Am. Math. Soc. 110 (1990), 789-798. Zbl 0721.47013, MR 1027097, 10.2307/2047922 |
| Reference:
|
[7] Labrousse, J. P.: On a metric space of closed operators on a Hilbert space.Univ. Nac. Tucumán, Rev., Ser. A 16 (1966), 45-77. Zbl 0154.15803, MR 0226445 |
| Reference:
|
[8] Labrousse, J. P.: Quelques topologies sur des espaces d'opérateurs dans des espaces de Hilbert et leurs applications.Faculté des Sciences de Nice (Math.) 1 (1970), 47 pages. |
| Reference:
|
[9] Lambert, A., Petrovic, S.: Beyond hyperinvariance for compact operators.J. Funct. Anal. 219 (2005), 93-108. Zbl 1061.47018, MR 2108360, 10.1016/j.jfa.2004.06.001 |
| Reference:
|
[10] Singh, R. K., Manhas, J. S.: Composition Operators on Function Spaces.North-Holland Mathematics Studies 179. North-Holland, Amsterdam (1993). Zbl 0788.47021, MR 1246562 |
| . |
