Banach Orlicz Algebras on a Locally Compact Group
Let G be a locally compact group with a fixed left Haar measure l. Given an N function ph, we consider the Orlicz space {L^\varphi}(G) under the convolution multiplication and establish that, for amenable groups under mild conditions on ph, it is a convolution algebra if and only if G is compact. Also we prove that for a locally compact group G, the convolution algebra {L^\varphi}(G) has a bounded approximate identity if and only if G is discrete.