The Socle and finite dimensionality of some Banach algebras |
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Authors: | Ali Ghaffari Ali Reza Medghalchi |
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Institution: | (1) Department of Mathematics, Semnan University, Semnan, Iran |
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Abstract: | 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 groupG, G is compact if there exists a measure μ in Soc(L
1(G)) such that μ(G) ≠ 0. We also prove thatG is finite if Soc(M(G)) is closed and every nonzero left ideal inM(G) contains a minimal left ideal. |
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Keywords: | Banach algebras Socle finite dimensional locally compact group |
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