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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

Embedding the weighted space $Hv_0(G, E)$ of holomorphic functions into the sequence space $c_0(E)$

El Mustapha El Abbassi(Mohammed V University of Rabat)0000-0002-1865-6118
Lahbib Oubbı(Mohammed V University of Rabat)0000-0003-2119-9293
Pages
—
Publication Date
2020-12-08
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.

📌 3 Key Takeaways

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Objective & Hypothesis:We embed almost isometrically the generalized weighted space $Hv_0(G, E)$ of holomorphic functions on an open subset $G$ of $\mathbb{C}^N$ with values in a Banach space $E$, into $c_0(E)$, the space of all null sequences in $E$, where $v$ is an operator-valued continuous function on $G$ vanishing nowhere.
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Key Findings & Data:This extends and generalizes some known results in the literature.
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Conclusion & Impact:We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weighted spaces of holomorphic functions · Vector-valued holomorphic function · Operator-valued weights

Abstract

We embed almost isometrically the generalized weighted space $Hv_0(G, E)$ of holomorphic functions on an open subset $G$ of $\mathbb{C}^N$ with values in a Banach space $E$, into $c_0(E)$, the space of all null sequences in $E$, where $v$ is an operator-valued continuous function on $G$ vanishing nowhere. This extends and generalizes some known results in the literature. We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.

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Cite This Article

Abbassi, E. M. E., Oubbı, L. (2020). Embedding the weighted space $Hv_0(G, E)$ of holomorphic functions into the sequence space $c_0(E)$. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.621628

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