| Title:
|
Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space (English) |
| Author:
|
Diagana, Toka |
| Author:
|
McNeal, George D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
385-400 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper is concerned with the spectral analysis for the class of linear operators $A = D_\lambda + X \otimes Y$ in non-archimedean Hilbert space, where $D_\lambda$ is a diagonal operator and $X \otimes Y$ is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra. (English) |
| Keyword:
|
spectral analysis |
| Keyword:
|
diagonal operator |
| Keyword:
|
rank one operator |
| Keyword:
|
eigenvalue |
| Keyword:
|
spectrum |
| Keyword:
|
non-archimedean Hilbert space |
| MSC:
|
42A75 |
| MSC:
|
42A85 |
| MSC:
|
44A35 |
| idZBL:
|
Zbl 1212.47126 |
| idMR:
|
MR2573412 |
| . |
| Date available:
|
2009-09-23T21:34:41Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134911 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/137453 |
| . |
| Reference:
|
[1] Basu S., Diagana T., Ramaroson F.: A $p$-adic version of Hilbert-Schmidt operators and applications.J. Anal. Appl. 2 (2004), no. 3, 173--188. Zbl 1077.47061, MR 2092641 |
| Reference:
|
[2] Attimu D., Diagana T.: Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II.Comment. Math. Univ. Carolin. 48 (2007), no. 3, 431--442. MR 2374125 |
| Reference:
|
[3] Diagana T.: Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications.Ann. Math. Blaise Pascal 12 (2005), no. 1, 205--222. Zbl 1087.47061, MR 2126449, 10.5802/ambp.203 |
| Reference:
|
[4] Diagana T.: Erratum to: ``Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications".Ann. Math. Blaise Pascal 13 (2006), 105--106. MR 2233015, 10.5802/ambp.217 |
| Reference:
|
[5] Diagana T.: Non-Archimedean Linear Operators and Applications.Nova Science Publishers, Huntington, NY, 2007. Zbl 1112.47060, MR 2294736 |
| Reference:
|
[6] Diagana T.: Representation of bilinear forms in non-archimedean Hilbert space by linear operators.Comment. Math. Univ. Carolin. 47 (2006), no. 4, 695--705. MR 2337423 |
| Reference:
|
[7] Diagana T.: An Introduction to Classical and $p$-adic Theory of Linear Operators and Applications.Nova Science Publishers, New York, 2006. Zbl 1118.47323, MR 2269328 |
| Reference:
|
[8] Diarra B.: An operator on some ultrametric Hilbert spaces.J. Analysis 6 (1998), 55--74. Zbl 0930.47049, MR 1671148 |
| Reference:
|
[9] Diarra B.: Geometry of the $p$-adic Hilbert spaces.preprint, 1999. |
| Reference:
|
[10] Fois C., Jung I.B., Ko E., Pearcy C.: On rank one perturbations of normal operators.J. Funct. Anal. 253 (2008), 628--646. MR 2370093, 10.1016/j.jfa.2007.09.007 |
| Reference:
|
[11] Ionascu E.: Rank-one perturbations of diagonal operators.Integral Equations Operator Theory 39 (2001), 421--440. Zbl 0979.47012, MR 1829279, 10.1007/BF01203323 |
| Reference:
|
[12] Keller H.A., Ochsenius H.: Bounded operators on non-archimedean orthomodular spaces.Math. Slovaca 45 (1995), no. 4, 413--434. Zbl 0855.46049, MR 1387058 |
| Reference:
|
[13] Ochsenius H., Schikhof W.H.: Banach spaces over fields with an infinite rank valuation.$p$-adic Functional Analysis (Poznan, 1998), Lecture Notes in Pure and Appl. Mathematics, 207, Marcel Dekker, New York, 1999, pp. 233--293. Zbl 0938.46056, MR 1703500 |
| Reference:
|
[14] van Rooij A.C.M.: Non-archimedean Functional Analysis.Marcel Dekker, New York, 1978. Zbl 0396.46061, MR 0512894 |
| . |
