Open Access
December 2007 Non-Archimedean Hilbert like spaces
J. Aguayo, M. Nova
Bull. Belg. Math. Soc. Simon Stevin 14(5): 787-797 (December 2007). DOI: 10.36045/bbms/1197908895


Let $\mathbb{K}$ be a non-Archimedean, complete valued field. It is known that the supremum norm $\left\Vert \cdot\right\Vert _{\infty}$ on $c_{0}$ is induced by an inner product if and only if the residual class field of $\mathbb{K}$ is formally real. One of the main problems of this inner product is that $c_{0}$ is not orthomodular, as is any classical Hilbert space. Our goal in this work is to identify those closed subspaces of $c_{0}$ which have a normal complement. In this study we also involve projections, adjoint and self-adjoint operators.


Download Citation

J. Aguayo. M. Nova. "Non-Archimedean Hilbert like spaces." Bull. Belg. Math. Soc. Simon Stevin 14 (5) 787 - 797, December 2007.


Published: December 2007
First available in Project Euclid: 17 December 2007

zbMATH: 1134.46011
MathSciNet: MR2378989
Digital Object Identifier: 10.36045/bbms/1197908895

Primary: 46C50
Secondary: ‎46S10

Keywords: adjoint and selfadjoint operators , inner products , Non-archimedean fields , normal complemented subspaces , projections

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 5 • December 2007
Back to Top