Vol. 62, No. 2, 1976

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Homomorphisms of group algebras with squared norm less than

Nigel Kalton and G. V. Wood

Vol. 62 (1976), No. 2, 439–460

We show that two locally compact abelian groups G1 and G2 are isomorphic if there exists an aigebra isomorphism T of L1(G1) onto L1(G2) with T< √2-. 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 give a representation theorem for isomorphisms satisfying T< √2-.

Mathematical Subject Classification 2000
Primary: 43A20
Received: 30 June 1975
Published: 1 February 1976
Nigel Kalton
Department of Mathematics
University of Missouri
Columbia MO 65211
United States
G. V. Wood