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arXiv · 1807.02849

On some study of the fine spectra of generalized difference operator $\Delta_{a,b}$ on $\ell_p \ (1<p<\infty)$

Riddhick Birbonshi·Arnab Patra·P. D. Srivastava
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Abstract

In this paper, we determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the generalized difference operator $\Delta_{a,b}$ on the sequence space $\ell_p \ (1< p < \infty)$ where the real sequences $a=\{a_k\}$ and $b=\{b_k\}$ are not necessarily convergent. Hence our results generalize the work given by Akhmedov and El-Shabrawy [Math. Slovaca 65~(5) (2015) 1137--1152] for the sequence space $\ell_p (1< p <\infty)$.

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Riddhick Birbonshi, Arnab Patra, P. D. Srivastava. 2018-07-08. On some study of the fine spectra of generalized difference operator $\Delta_{a,b}$ on $\ell_p \ (1<p<\infty)$. https://arxiv.org/abs/1807.02849

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