Weak amenability of weighted Orlicz algebras

Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$, the weak amenability is obtained under conditions similar to the one considered by Y. Zhang for weighted group algebras. Our methods can be applied to various families of weighted Orlicz algebras, including weighted $L^p$-spaces

Chaotic translations on weighted Orlicz spaces

Let $G$ be a locally compact group, $w$ be a weight on $G$ and $\Phi$ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^\Phi(G)$. In particular, transitivity is equivalent to the blow-up/collapse property in our case. Moreover, the dense set of periodic elements implies transitivity automatically

Multipliers of Banach valued weighted function spaces

We generalize Banach valued spaces to Banach valued weighted function spaces and study the multipliers space of these spaces. We also show the relationship between multipliers and tensor product of Banach valued weighted function spaces