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Nonseparability and uniform structures in locally compact groups
1995
Let G be a locally compact topological group. We prove that if G is not a SIN-group, then the quotient Banach space &L(G)/1&(G) contains an isometric linear copy of 1? . To get this result, we first establish an extension theorem for (bilaterally) uniformly continuous functions on G.
Keywords:
- Riesz–Markov–Kakutani representation theorem
- Vague topology
- Locally compact group
- Radon measure
- Locally compact space
- Noncommutative harmonic analysis
- Mathematical analysis
- Mathematics
- Continuous functions on a compact Hausdorff space
- Banach–Alaoglu theorem
- Topology
- Compact space
- Uniform continuity
- Topological group
- Combinatorics
- Discrete mathematics
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