Finite-dimensional Left Ideals in Some Algebras Associated with a Locally Compact Group
نویسندگان
چکیده
Let G be a locally compact group, let L1(G) be its group algebra, let M(G) be its usual measure algebra, let L1(G)∗∗ be the second dual of L1(G) with an Arens product, and let LUC(G)∗ be the conjugate of the space LUC(G) of bounded, left uniformly continuous, complex-valued functions on G with an Arens-type product. We find all the finite-dimensional left ideals of these algebras. We deduce that such ideals exist in L1(G) and M(G) if and only if G is compact, and in L1(G)∗∗ (except those generated by right annihilators of L1(G)∗∗) and LUC(G)∗ if and only if G is amenable.
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