In this study, we give certain characterizations of matrix transformations from the paranormed space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ to one of the classical sequence spaces $c_{0},c,l_{\infty }.$ Also, we show that such matrix operators are bounded linear operators.
📌 3 Key Takeaways
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Objective & Hypothesis:In recent paper, the space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ which is the generalization of the absolute Euler Space on the space $l(\mu)$, has been introduced and studied by Gökçe and Sarıgöl [3].
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Key Findings & Data:In recent paper, the space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ which is the generalization of the absolute Euler Space on the space $l(\mu)$, has been introduced and studied by Gökçe and Sarıgöl [3].
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Conclusion & Impact:In this study, we give certain characterizations of matrix transformations from the paranormed space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ to one of the classical sequence spaces $c_{0},c,l_{\infty }.$ Also, we show that such matrix operators are bounded linear operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Euler means · absolute summability · matrix transformations
Abstract
In recent paper, the space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ which is the generalization of the absolute Euler Space on the space $l(\mu)$, has been introduced and studied by Gökçe and Sarıgöl [3]. In this study, we give certain characterizations of matrix transformations from the paranormed space $ \left\vert E_{\phi}^{r}\right\vert (\mu)$ to one of the classical sequence spaces $c_{0},c,l_{\infty }.$ Also, we show that such matrix operators are bounded linear operators.
Gökçe, F. (2022). Matrix Operators on the Absolute Euler space $\left\vert E_{\phi }^{r}\right\vert (\mu)$. Turkish Journal of Mathematics and Computer Science, Volume: 14 Issue: 1. https://doi.org/10.47000/tjmcs.1007885
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