Albert Kubzdela

On non-Archimedean Hilbertian spaces

Abstract We consider a special class of non-Archimedean Banach spaces, called Hilbertian, for which every one-dimensional linear subspace has an orthogonal complement. We prove that all immediate extensions of c o , contained in l ∞ , are Hilbertian. In this way we construct examples of Hilbertian spaces over a non-spherically complete valued field without an orthogonal base.

On multi-orthogonal bases in finite-dimensional non-Archimedean normed spaces

The paper deals with the problem of the existence multi-orthogonal bases in finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field.

On orthocomplemented subspaces in p-adic Banach spaces

Abstract For linear subspaces of finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field which is not spherically complete, we study orthocomplementation as related to strictness and the Hahn-Banach property. We prove that there exist finite-dimensional normed spaces which possess non-orthocomplemented, strict HB-subspaces.