Representation of bilinear forms in non-Archimedean Hilbert space by linear operators

Toka Diagana

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 4, page 695-705
  • ISSN: 0010-2628

Abstract

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The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if φ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then φ is representable by a unique self-adjoint (possibly unbounded) operator A .

How to cite

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Diagana, Toka. "Representation of bilinear forms in non-Archimedean Hilbert space by linear operators." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 695-705. <http://eudml.org/doc/249834>.

@article{Diagana2006,
abstract = {The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if $\phi $ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then $\phi $ is representable by a unique self-adjoint (possibly unbounded) operator $A$.},
author = {Diagana, Toka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {non-Archimedean Hilbert space; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form; bounded bilinear form; self-adjoint operator; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form},
language = {eng},
number = {4},
pages = {695-705},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Representation of bilinear forms in non-Archimedean Hilbert space by linear operators},
url = {http://eudml.org/doc/249834},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Diagana, Toka
TI - Representation of bilinear forms in non-Archimedean Hilbert space by linear operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 4
SP - 695
EP - 705
AB - The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if $\phi $ is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then $\phi $ is representable by a unique self-adjoint (possibly unbounded) operator $A$.
LA - eng
KW - non-Archimedean Hilbert space; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form; bounded bilinear form; self-adjoint operator; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form
UR - http://eudml.org/doc/249834
ER -

References

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  1. Cassels J.W.S., Local Fields, London Mathematical Society, Student Texts 3, Cambridge Univ. Press, London, 1986. Zbl0595.12006MR0861410
  2. Basu S., Diagana T., Ramaroson F., A p -adic version of Hilbert-Schmidt operators and applications, J. Anal. Appl. 2 (2004), 3 173-188. (2004) Zbl1077.47061MR2092641
  3. de Bivar-Weinholtz A., Lapidus M.L., Product formula for resolvents of normal operator and the modified Feynman integral, Proc. Amer. Math. Soc. 110 (1990), 2 449-460. (1990) MR1013964
  4. Diagana T., Towards a theory of some unbounded linear operators on p -adic Hilbert spaces and applications, Ann. Math. Blaise Pascal 12 (2005), 1 205-222. (2005) Zbl1087.47061MR2126449
  5. 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. (2006) MR2233015
  6. Diagana T., Bilinear forms on non-Archimedean Hilbert spaces, preprint, 2005. 
  7. Diagana T., Fractional powers of the algebraic sum of normal operators, Proc. Amer. Math. Soc. 134 (2006), 6 1777-1782. (2006) Zbl1092.47027MR2207493
  8. Diarra B., An operator on some Ultrametric Hilbert spaces, J. Anal. 6 (1998), 55-74. (1998) Zbl0930.47049MR1671148
  9. Diarra B., Geometry of the p -adic Hilbert spaces, preprint, 1999. 
  10. Johnson G.W., Lapidus M.L., The Feynman Integral and Feynman Operational Calculus, Oxford Univ. Press, Oxford, 2000. MR1771173
  11. Kato T., Perturbation Theory for Linear Operators, Springer, New York, 1966. Zbl0836.47009MR0203473
  12. Ochsenius H., Schikhof W.H., Banach spaces over fields with an infinite rank valuation, -adic Functional Analysis (Poznan, 1998), Marcel Dekker, New York, 1999, pp.233-293. Zbl0938.46056MR1703500
  13. van Rooij A.C.M., Non-Archimedean Functional Analysis, Marcel Dekker, New York, 1978. Zbl0396.46061MR0512894

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