The size of the quotient LUC(G)/UC(G)
-
Mahmoud Filali
and
Pekka Salmi
Abstract
We consider the Banach space LUC(G) (RUC(G)) of the bounded left (right) uniformly continuous functions on a locally compact group G, the Banach space UC(G) = LUC(G)∩RUC(G) of the bounded uniformly continuous functions on G and the quotient Banach space LUC(G)/UC(G). If G is a sin group, that is, the right and the left uniformities coincide, then the quotient LUC(G)/UC(G) is trivial, so we are concerned with non-sin groups. We bring up the topological structure of G to the Banach space structure of the quotient by showing first that when the compact covering number k(G) is greater than or equal to the local weight b(G), there is a linear isometric copy of 
in LUC(G)/UC(G). Then, using the generalised Kakutani–Kodaira theorem due to Zhiguo Hu, we deduce that in the case of a general non-sin group, there exists a compact normal subgroup N of G such that ℵ0 ≤ b(G/N) ≤ k(G) and LUC(G)/UC(G) contains a linear isometric copy of 
.
© de Gruyter 2011
Articles in the same Issue
- The generalized conjugacy problem for virtually free groups
- Stably diffeomorphic manifolds and l2q+1(ℤ[π])
- The size of the quotient LUC(G)/UC(G)
- Finitistic dimension conjecture and conditions on ideals
- Principal 2-bundles and their gauge 2-groups
- Flat covers over formal triangular matrix rings and minimal Quillen factorizations
- Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry
- Algebraic Bol loops
Articles in the same Issue
- The generalized conjugacy problem for virtually free groups
- Stably diffeomorphic manifolds and l2q+1(ℤ[π])
- The size of the quotient LUC(G)/UC(G)
- Finitistic dimension conjecture and conditions on ideals
- Principal 2-bundles and their gauge 2-groups
- Flat covers over formal triangular matrix rings and minimal Quillen factorizations
- Maximal holonomy of infra-nilmanifolds with 3-dimensional Iwasawa geometry
- Algebraic Bol loops
