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We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra… (More)
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 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 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)
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)