Denote by c = 2 ℵ 0 the cardinal of continuum. We construct an intriguing family (Pα : α ∈ c) of prime z-ideals in C 0 (R) with the following properties: • If f ∈ P i 0 for some i 0 ∈ c, then f ∈ P i for all but finitely many i ∈ c; • T i =i 0 P i ⊂ P i 0 for each ı 0 ∈ c. We also construct a well-ordered increasing chain, as well as a well-ordered… (More)
We investigate possible preduals of the measure algebra M (G) of a locally compact group and the Fourier algebra A(G) of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak *-continuous so that these algebras are dual Banach algebras. In this paper we find… (More)
We give a description of the continuity ideals and the kernels of homomorphisms from the algebras of continuous functions on locally compact spaces into Banach algebras.
We show that a locally compact group is amenable if and only if it admits a (nontrivial) injective Banach module which is reflexive as a Banach space, generalizing work
For a locally compact group G, the measure convolution algebra M (G) carries a natural coprod-uct. In previous work, we showed that the canonical predual C0(G) of M (G) is the unique predual which makes both the product and the coproduct on M (G) weak *-continuous. Given a discrete semi-group S, the convolution algebra ℓ 1 (S) also carries a coproduct. In… (More)