Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications

Toka Diagana[1]

  • [1] Howard University Department of Mathematics 2441 6th Street N.W. Washington, D.C. 20059 U.S.A.

Annales mathématiques Blaise Pascal (2005)

  • Volume: 12, Issue: 1, page 205-222
  • ISSN: 1259-1734

Abstract

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We are concerned with some unbounded linear operators on the so-called p -adic Hilbert space 𝔼 ω . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on 𝔼 ω , and the solvability of the equation A u = v where A is a linear operator on 𝔼 ω .

How to cite

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Diagana, Toka. "Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications." Annales mathématiques Blaise Pascal 12.1 (2005): 205-222. <http://eudml.org/doc/10513>.

@article{Diagana2005,
abstract = {We are concerned with some unbounded linear operators on the so-called $p$-adic Hilbert space $\mathbb\{E\}_\omega $. Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on $\mathbb\{E\}_\omega $, and the solvability of the equation $Au = v$ where $A$ is a linear operator on $\mathbb\{E\}_\omega $.},
affiliation = {Howard University Department of Mathematics 2441 6th Street N.W. Washington, D.C. 20059 U.S.A.},
author = {Diagana, Toka},
journal = {Annales mathématiques Blaise Pascal},
keywords = {-adic Hilbert space; free Banach space},
language = {eng},
month = {1},
number = {1},
pages = {205-222},
publisher = {Annales mathématiques Blaise Pascal},
title = {Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications},
url = {http://eudml.org/doc/10513},
volume = {12},
year = {2005},
}

TY - JOUR
AU - Diagana, Toka
TI - Towards a theory of some unbounded linear operators on $p$-adic Hilbert spaces and applications
JO - Annales mathématiques Blaise Pascal
DA - 2005/1//
PB - Annales mathématiques Blaise Pascal
VL - 12
IS - 1
SP - 205
EP - 222
AB - We are concerned with some unbounded linear operators on the so-called $p$-adic Hilbert space $\mathbb{E}_\omega $. Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on $\mathbb{E}_\omega $, and the solvability of the equation $Au = v$ where $A$ is a linear operator on $\mathbb{E}_\omega $.
LA - eng
KW - -adic Hilbert space; free Banach space
UR - http://eudml.org/doc/10513
ER -

References

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  1. S. Albeverio, J. M. Bayod, C. Perez-Gargia, R. Cianci, A. Y. Khrennikov, Non-Archimedean Analogues of Orthogonal and Symmetric Operators and p -adic Quantization, Acta Appl. Math. 57 (1999), 205-237 Zbl0943.46044MR1722049
  2. S. Basu, T. Diagana, F. Ramaroson, A p -adic Version of Hilbert-Schmidt Operators and Applications, J. Anal. Appl. 2 (2004), 173-188 Zbl1077.47061MR2092641
  3. B. Diarra, S. Ludkovsky, Spectral Integration and Spectral Theory for Non-Archimedean Banach Spaces, Int. J. Math. Math. Sci. 31 (2002), 421-442 Zbl0999.47063MR1926812
  4. B. Diarra, An Operator on Some Ultrametric Hilbert spaces, J. Analysis 6 (1998), 55-74 Zbl0930.47049MR1671148
  5. B. Diarra, Geometry of the p -adic Hilbert Spaces, Preprint (1999) Zbl0943.46047
  6. H. A. Keller, H. Ochsenius, Algebras of Bounded Operators on nonclassical orthomodular spaces. Proceedings of the International Quantum Structures Association, Part III (Castiglioncello, 1992), Internat. J. Theoret. Phys. 33 (1994), 1-11 Zbl0809.46094MR1263295
  7. A. Y. Khrennikov, Mathematical Methods in Non-Archimedean Physics. (Russian)., Uspekhi Math. Nauk. 45 (1990), 79-110 Zbl0722.46040MR1075387
  8. A. Y. Khrennikov, Generalized Functions on a Non-Archimedean Super Space, (Russian) Izv. Akad. Nauk SSSR Ser. Math. 55 (1991), 1257-1286 Zbl0755.46048MR1152212
  9. A. Y. Khrennikov, p -adic Quantum Mechanics with p -adic Valued Functions, J. Math. Phys. 32 (1991), 932-937 Zbl0746.46067MR1097779
  10. H. Ochsenius, W. H. Schikhof, Banach Spaces Over Fields With An Infinite Rank Valuation, p -adic Functional Analysis (Poznań, 1998), Lectures Notes in Pure and Appl. Math. 207 (1999), 233-293 Zbl0938.46056MR1703500
  11. A. C. M. van Rooij, Non-Archimedean Functional Analysis, (1978), Marcel Dekker, Inc. Zbl0396.46061MR512894

Citations in EuDML Documents

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  1. Toka Diagana, Erratum to: “Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications”
  2. Toka Diagana, Representation of bilinear forms in non-Archimedean Hilbert space by linear operators
  3. Dodzi Attimu, Toka Diagana, Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II
  4. Toka Diagana, George D. McNeal, Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
  5. Dodzi Attimu, Toka Diagana, Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces

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