Malaysian Journal of Mathematical Sciences, August 2012, Vol. 6(S)
Special Issue: International Workshop on Mathematical Analysis (IWOMA)
Subdivision of the Spectra for Difference Operator over Certain Sequence Space
Feyzi Başar, Nuh Durna and Mustafa Yildirim
Corresponding Email: [email protected]
Received date: -
Accepted date: -
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 \(\Delta\) over the sequence spaces \(c_0\) , \(c\), \(\ell_{p}\) and \(b\upsilon_p\) are determined, where \(b\upsilon_p\) denotes the space of all sequences (\(k_x\) ) such that \((x_{k}-x_{k-1})\) belongs to the sequence space \(\ell_{p}\) and \(1 < p < \infty\).
Keywords: Spectrum, fine spectrum, approximate point spectrum, defect spectrum, compression spectrum, difference operator
