Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space

Toka Diagana; George D. McNeal

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 3, page 385-400
  • ISSN: 0010-2628

Abstract

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The paper is concerned with the spectral analysis for the class of linear operators A = D λ + X ⊗ Y in non-archimedean Hilbert space, where D λ is a diagonal operator and X ⊗ Y is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.

How to cite

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Diagana, Toka, and McNeal, George D.. "Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space." Commentationes Mathematicae Universitatis Carolinae 50.3 (2009): 385-400. <http://eudml.org/doc/33322>.

@article{Diagana2009,
abstract = {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.},
author = {Diagana, Toka, McNeal, George D.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {spectral analysis; diagonal operator; rank one operator; eigenvalue; spectrum; non-archimedean Hilbert space; non-Archimedean Hilbert space; spectral analysis; diagonal operator; rank one operator},
language = {eng},
number = {3},
pages = {385-400},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space},
url = {http://eudml.org/doc/33322},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Diagana, Toka
AU - McNeal, George D.
TI - Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 3
SP - 385
EP - 400
AB - 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.
LA - eng
KW - spectral analysis; diagonal operator; rank one operator; eigenvalue; spectrum; non-archimedean Hilbert space; non-Archimedean Hilbert space; spectral analysis; diagonal operator; rank one operator
UR - http://eudml.org/doc/33322
ER -

References

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  5. Diagana T., Non-Archimedean Linear Operators and Applications, Nova Science Publishers, Huntington, NY, 2007. Zbl1112.47060MR2294736
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  7. Diagana T., An Introduction to Classical and p -adic Theory of Linear Operators and Applications, Nova Science Publishers, New York, 2006. Zbl1118.47323MR2269328
  8. Diarra B., An operator on some ultrametric Hilbert spaces, J. Analysis 6 (1998), 55--74. Zbl0930.47049MR1671148
  9. Diarra B., Geometry of the p -adic Hilbert spaces, preprint, 1999. 
  10. Fois C., Jung I.B., Ko E., Pearcy C., 10.1016/j.jfa.2007.09.007, J. Funct. Anal. 253 (2008), 628--646. MR2370093DOI10.1016/j.jfa.2007.09.007
  11. Ionascu E., 10.1007/BF01203323, Integral Equations Operator Theory 39 (2001), 421--440. Zbl0979.47012MR1829279DOI10.1007/BF01203323
  12. Keller H.A., Ochsenius H., Bounded operators on non-archimedean orthomodular spaces, Math. Slovaca 45 (1995), no. 4, 413--434. Zbl0855.46049MR1387058
  13. Ochsenius H., Schikhof W.H., Banach spaces over fields with an infinite rank valuation, -adic Functional Analysis (Poznan, 1998), Lecture Notes in Pure and Appl. Mathematics, 207, Marcel Dekker, New York, 1999, pp. 233–293. Zbl0938.46056MR1703500
  14. van Rooij A.C.M., Non-archimedean Functional Analysis, Marcel Dekker, New York, 1978. Zbl0396.46061MR0512894

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