Homomorphisms of Group Algebras with Norm Less than V2
نویسنده
چکیده
We show that two locally compact abelian groups Gx and G2 are isomorphic if there exists an algebra isomorphism T of L\Gλ) onto L\G2) with | | Γ | | < V2. This constant is best possible. The same result is proved for locally compact connected groups, but for the general locally compact group, the result is proved under the hypothesis | |T | |< 1.246. Similar results are given for the algebras C{G) and L~(G) when G is compact. In the abelian case, we giveji representation theorem for isomorphisms satisfying ||T|| < λ/2.
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