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Keywords:
non-Archimedean Hilbert space; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form; bounded bilinear form; self-adjoint operator
non-Archimedean Hilbert space; non-Archimedean bilinear form; unbounded operator; unbounded bilinear form; bounded bilinear form; self-adjoint operator
Summary:
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 $A$.
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References:
[1] Cassels J.W.S.: Local Fields. London Mathematical Society, Student Texts 3, Cambridge Univ. Press, London, 1986. MR 0861410 | Zbl 0595.12006
[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. MR 2092641 | Zbl 1077.47061
[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. MR 1013964
[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. MR 2126449 | Zbl 1087.47061
[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. MR 2233015
[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. MR 2207493 | Zbl 1092.47027
[8] Diarra B.: An operator on some Ultrametric Hilbert spaces. J. Anal. 6 (1998), 55-74. MR 1671148 | Zbl 0930.47049
[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. MR 1771173
[11] Kato T.: Perturbation Theory for Linear Operators. Springer, New York, 1966. MR 0203473 | Zbl 0836.47009
[12] Ochsenius H., Schikhof W.H.: Banach spaces over fields with an infinite rank valuation. $p$-adic Functional Analysis (Poznan, 1998), Marcel Dekker, New York, 1999, pp.233-293. MR 1703500 | Zbl 0938.46056
[13] van Rooij A.C.M.: Non-Archimedean Functional Analysis. Marcel Dekker, New York, 1978. MR 0512894 | Zbl 0396.46061
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