Non-Archimedean Hilbert like spaces

被引：6

作者：

Aguayo, J. ^{[1
]}

Nova, M. ^{[1
]}

机构：

[1] Univ Catolica Santisima Concepcion, Fac Ingn, Dept Ciencias Basic, Concepcion 160, Chile

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2007年 / 14卷 / 05期

关键词：

non-archimedean fields; inner products; normal complemented sub-spaces; projections; adjoint and selfadjoint operators;

D O I：

10.36045/bbms/1197908895

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a non-Archimedean, complete valued field. It is known that the supremum norm ||.||(infinity) on c(0) is induced by an inner product if and only if the residual class field of 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.

引用

页码：787 / 797

页数：11