Subdivision of the spectra for difference operator over certain sequence space

Abstract

In a series of papers, B. Altay, F. Basar and A. M. Akhmedov recently investigated the spectra and fine spectra for difference operator, considered as bounded operator over various sequence spaces. In the present paper approximation point spectrum, defect spectrum and compression spectrum of difference operator ? over the sequence spaces c 0, c, ? p and b? p are determined, where b? p denotes the space of all sequences (x k) such that (x k-x k-1) belongs to the sequence space ? p and 1 < p <?.