TY  - JOUR
AB  - The class [S] of locally compact groups G is considered, for which the algebra L to the power of 1(G) is symmetric (=Hermitian). It is shown that [S] is stable under semidirect compact extensions, i.e., H Epsilon [S] and K compact implies K xs H Epsilon [S]. For connected solvable Lie groups inductive conditions for symmetry are given. A construction for nonsymmetric Banach algebras is given which shows that there exists exactly one connected and simply solvable Lie group of dimension less-than-or-equals 4 which is not in [S]. This example shows that G/Z Epsilon [S], Z the center of G, in general does not imply G Epsilon [S]. It is shown that nevertheless for discrete groups and a (possibly) stronger form of symmetry this implication holds, implying a new and shorter proof of the fact that [S] contains all discrete nilpotent groups.
DA  - 1979
DO  - 10.1016/0022-1236(79)90107-1
LA  - eng
IS  - 2
M2  - 119
PY  - 1979
SN  - 0022-1236
SP  - 119-134
T2  - Journal of functional analysis
TI  - Symmetry and nonsymmetry for locally compact groups
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17754844
Y2  - 2024-11-22T08:14:39
ER  -