Finding The HK Completions of Some Sequence Spaces

Husain Alhayek

Hama University, Department of Mathematics, Hama, Syria

Emails: Hayekalhusain333@gmail.com

Abstract

In this paper, we prove the following result: If the space  (the finite sequences) is equipped with the norm which is naturally induced by a positive definite Hermitian and diagonally blockwise constructed matrix, then an HK completion exists. Also, we investigate our result through many illustrated examples.

Keywords: HK completion; vector space; normed space; sequence