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

Authors : El Mustapha El Abbassi, Lahbib OUBBI

Pages : 2063-2070

Doi:10.15672/hujms.621628

View : 14 | Download : 9

Publication Date : 2020-12-08

Article Type : Research Paper

Abstract :We embed almost isometrically the generalized weighted space $Hv_0insert ignore into journalissuearticles values(G, E);$ of holomorphic functions on an open subset $G$ of $\mathbb{C}^N$ with values in a Banach space $E$, into $c_0insert ignore into journalissuearticles values(E);$, 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.
Keywords : Weighted spaces of holomorphic functions, Vector valued holomorphic function, Operator valued weights, Almost isometric embedding