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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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].
📌 3 Key Takeaways
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Objective & Hypothesis: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 < ∞.
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Key Findings & Data: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 < ∞.
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Conclusion & Impact: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].
🔬Design:Research Article
📍Scope:2008 Verileri
⚙️Variables:Spectrum of an operator · double sequential band matrix · spectral mapping theorem
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].
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Cite This Article
BAŞAR, F., KARAİSA, A. (2015). On the fine spectrum of the generalized difference operator defined by a double sequential band matrix over the sequence space $\ell_p$, (1 < p < ∞). Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 6, 1315–1332. https://ajindex.com/articles/669509