The Socle and finite dimensionality of some Banach algebras
نویسندگان
چکیده
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group G, G is compact if there exists a measure μ in Soc(L1(G)) such that μ(G) 6= 0. We also prove that G is finite if Soc(M(G)) is closed and every nonzero left ideal in M(G) contains a minimal left ideal.
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