Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
spectral analysis; diagonal operator; rank one operator; eigenvalue; spectrum; non-archimedean Hilbert space
spectral analysis; diagonal operator; rank one operator; eigenvalue; spectrum; non-archimedean Hilbert space
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.
Related articles:
References:
[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. MR 2092641 | Zbl 1077.47061
[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
[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. DOI 10.5802/ambp.203 | MR 2126449 | Zbl 1087.47061
[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. DOI 10.5802/ambp.217 | MR 2233015
[5] Diagana T.: Non-Archimedean Linear Operators and Applications. Nova Science Publishers, Huntington, NY, 2007. MR 2294736 | Zbl 1112.47060
[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
[7] Diagana T.: An Introduction to Classical and $p$-adic Theory of Linear Operators and Applications. Nova Science Publishers, New York, 2006. MR 2269328 | Zbl 1118.47323
[8] Diarra B.: An operator on some ultrametric Hilbert spaces. J. Analysis 6 (1998), 55--74. MR 1671148 | Zbl 0930.47049
[9] Diarra B.: Geometry of the $p$-adic Hilbert spaces. preprint, 1999.
[10] Fois C., Jung I.B., Ko E., Pearcy C.: On rank one perturbations of normal operators. J. Funct. Anal. 253 (2008), 628--646. DOI 10.1016/j.jfa.2007.09.007 | MR 2370093
[11] Ionascu E.: Rank-one perturbations of diagonal operators. Integral Equations Operator Theory 39 (2001), 421--440. DOI 10.1007/BF01203323 | MR 1829279 | Zbl 0979.47012
[12] Keller H.A., Ochsenius H.: Bounded operators on non-archimedean orthomodular spaces. Math. Slovaca 45 (1995), no. 4, 413--434. MR 1387058 | Zbl 0855.46049
[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. MR 1703500 | Zbl 0938.46056
[14] van Rooij A.C.M.: Non-archimedean Functional Analysis. Marcel Dekker, New York, 1978. MR 0512894 | Zbl 0396.46061
Search
Partner of
