arXiv subjects

Ibrahim Akbarbaglu

Publications and source records attributed to Ibrahim Akbarbaglu.

2 recordsLinked to original sources

arXiv2022

On the algebraic structures in $\A_Φ(G)$

Let $G$ be a locally compact group and $(Φ, Ψ)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Figà-Talamanca-Herz-Orlicz algebra ${\A}_Φ(G)$ is a Banach algebra under convolution product if and only if $G$ is compact. Then it is shown that ${\A}_Φ(G)$ is a Segal algebra, and as a consequence, the amenability of ${\A}_Φ(G)$ and the existence of a bounded approximate identity for ${\A}_Φ(G)$ under the convolution product is discussed. Furthermore, it is shown that for a compact abelian group $G$, the character space of ${\A}_Φ(G)$ under convolution product can be identified with $\widehat{G}$, the dual of $G$.

math.FA↗

arXiv2018

Topological transitive sequence of cosine operators on Orlicz space

For a Young function $ϕ$ and a locally compact second countable group $G,$ let $L^ϕ(G)$ denote the Orlicz space on $G.$ In this article, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators $\{C_n\}_{n=1}^{\infty}:=\{\frac{1}{2}(T^n_{g,w}+S^n_{g,w})\}_{n=1}^{\infty}$, defined on $L^ϕ(G)$. We investigate the conditions for a sequence of cosine operators to be topological mixing. Moreover, we go on to prove the similar results for the direct sum of a sequence of the cosine operators. At the last, an example of a topological transitive sequence of cosine operators is given.

math.FA↗