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In this paper, the conditions are considered that a weighted Orlicz space, L^Φ_w(G), is a Banach algebra with convolution as  multiplication in context of a locally compact σ-compact groups. We also for a class of Orlicz spaces, obtain an equivalent condition, such that a weighted Orlicz space to be a convolution Banach algebra. This resultes generalized some known results in Lebesgue spaces.

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Let $(pi,,H)$ be a unitary representation of $G$. Our interest to us here is the Banach space $WAP(pi)$; in particular,
we state some relations between $pi$ and any subrepresentation of $pi$ in this regard.