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Isomorphisms of Group Algebras
Author(s) -
Wood G. V.
Publication year - 1983
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/15.3.247
Subject(s) - mathematics , abelian group , isomorphism (crystallography) , group algebra , group (periodic table) , pure mathematics , conjecture , algebra over a field , locally compact group , locally compact space , combinatorics , chemistry , organic chemistry , crystal structure , crystallography
Let G 1 and G 2 be locally compact groups. If T is an algebra isomorphism of L 1 (G 1 ) onto L 1 (G 2 ) with ‖ T ‖ ⩽ ½(1+√3), then G 1 and G 2 are isomorphic. This improves on earlier results, and, in a certain sense, is best possible. However, the main conjecture that the groups are isomorphic if ‖ T ‖ < √2 remains unsolved except for abelian groups and for connected groups. Similar results are given for the measure algebra M ( G ) and for the algebra C ( G ) of continuous functions when the group G is compact.