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