A spectral theorem for a non-Archimedean valued field whose residue field is formally real
DOI:
https://doi.org/10.17398/Palabras clave:
self-adjoint operators, spectral theoremResumen
In this paper, we will prove a spectral theorem for self-adjoint compactoid operators. Also, we will study the condition on which the coefficient field must be imposed. In order to get the theorems, we will use the Fredholm theory for compactoid operators. Moreover, the property of maximal complete field is important for our study. These facts will allow us to find that the spectral theorem depends only on the residue class field, and is independent of the valuation group of the coefficient field. As a result, we can settle the problem of the spectral theorem in the case where the residue class field is formally real.
Descargas
Referencias
J. Aguayo, M. Nova, Non-Archimedean Hilbert like spaces, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 787 – 797.
J. Aguayo, M. Nova, Compact and self-adjoint operators on free Banach spaces of countable type, in “ Advances in non-Archimedean analysis ”, Contemp. Math., 665, Amer. Math. Soc., Providence, RI, 2016, 1 – 17.
J. Aguayo, M. Nova, K. Shamseddine, Characterization of compact and self-adjoint operators on free Banach spaces of countable type over the complex Levi-Civita field, J. Math. Phys. 54 (2) (2013), 19 pp.
E. Artin, “Algebraic numbers and algebraic functions”, Gordon and Breach Science Publishers, New York-London-Paris, 1967.
I. Kaplansky, Maximal fields with valuations, Duke Math. J. 9 (1942), 303 – 321.
H. Keller, H. Ochsenius, A spectral theorem for matrices over fields of power series, Ann. Math. Blaise Pascal 2 (1995), 169 – 179.
L. Narici, E. Beckenstein, A non-Archimedean inner product, in “Ultrametric functional analysis”, Contemp. Math., 384, American Mathematical Society, Providence, RI, 2005, 187 – 202.
B.H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202 – 252.
C. Perez-Garcı́a, W.H. Schikhof, “Locally convex spaces over non-Archimedean valued fields”, Cambridge Stud. Adv. Math., 119, Cambridge University Press, Cambridge, 2010.
W.H. Schikhof, “On p-adic compact operators”, Report 8911, pp. 1 – 28, Department of Mathematics, Catholic University, Nijmegen, The Netherlands, 1989.
O.F.G. Schilling, “The Theory of Valuations”, Math. Surveys, No. 4, American Mathematical Society, New York, 1950.
A.C.M. van Rooij, “Non-Archimedean functional analysis”, Monogr. Textbooks Pure Appl. Math., 51, Marcel Dekker, Inc., New York, 1978.
A.C.M. van Rooij, “Notes on p-adic Banach spaces”, I-V: Report 7633, pp. 1 – 62, Mathematisch Instituut, Katholieke Universiteit, Nijmegen, The Netherlands, 1976.
Descargas
Publicado
Número
Sección
Licencia
Derechos de autor 2024 The author
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
