On the fine spectrum of the generalized difference operator defined by a double sequential band matrix over the sequence space $\ell_p$, (1 < p < ∞)

Year 2015, Volume: 44 Issue: 6, 1315 - 1332, 01.12.2015

Feyzi Başar Ali Karaisa

Abstract

The main purpose of this paper is to determine the fine spectrum with
respect to the Goldberg’s classification of the operator $B(\tilde{r},\tilde{s})$ defined
by a double sequential band matrix over the sequence space $\ell_p$ where
1 < p < ∞. These results are more general than the spectrum of
the generalized difference operator B(r, s) over  $\ell_p$ of Bilgiç and Furkan
[Nonlinear Anal. 68(3)(2008), 499–506]. 

Keywords

Spectrum of an operator, double sequential band matrix, spectral mapping theorem, the sequence space lp, Goldberg’s classification

References

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