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.
Publié le : 2007-12-14
Classification:
Non-archimedean fields,
inner products,
normal complemented subspaces,
projections,
adjoint and selfadjoint operators,
46C50,
46S10
@article{1197908895,
author = {Aguayo, J. and Nova, M.},
title = {Non-Archimedean Hilbert like spaces},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 787-797},
language = {en},
url = {http://dml.mathdoc.fr/item/1197908895}
}
Aguayo, J.; Nova, M. Non-Archimedean Hilbert like spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 787-797. http://gdmltest.u-ga.fr/item/1197908895/