Hahn-Banach subspaces in Banach spaces with base.

Albert Kubzdela
Institute of Civil Engineering, Poznan University of Technology,
Ul. Piotrowo 5, 61-138 Poznan, Poland
e-mail: kubzdela@put.poznan.pl

Date:

We say that a closed subspace $D\subset E$ of Banach space E is a Hahn-Banach subspace (HB-subspace) of E, if each $f\in D^{\prime }$ has an extension $f_{0}\in E^{\prime }$ such that $\ \vert\vert f\vert\vert=\vert\vert f_{0}\vert\vert$. Ingleton's theorem says, that every subspace of an arbitrary Banach space over a spherically complete valued field K is a HB-subspace. We characterize Hahn-Banach subspaces in Banach spaces with base over a complete valued field K which is not spherically complete. We prove that every HB-subspace of countable type (or with countable codimension) in c₀(I) is orthocomplemented in c₀(I).