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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

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

El Mustapha El Abbassi
Lahbib Oubbi
Sayfa
2063–2070
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:This extends and generalizes some known results in the literature.
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Sonuç & Katkı:We then deduce the non 1-Hyers-Rassias stability of the isometry functional equation in the framework of Banach spaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Abbassi, E. M. E., Oubbi, L. (2022). Embedding the weighted space $Hv_0(G, E)$ of holomorphic functions into the sequence space $c_0(E)$. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 2063–2070. https://ajindex.com/articles/529603

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Kaynakça (13)

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