A -algebra without generalized topological divisors of zero
A characteristic property of the algebra .
A characterization of -algebras.
A characterization of
A characterization of commutative Fréchet algebras with all ideals closed
Let A be a commutative unital Fréchet algebra, i.e. a completely metrizable topological algebra. Our main result states that all ideals in A are closed if and only if A is a noetherian algebra
A characterization of essential sets of function algebras
In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space in terms of local properties of functions in at the points off .
A characterization of in terms of atoms
A characterization of maximal regular ideals in lmc algebras
A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
A characterization of the algebra of holomorphic functions on simply connected domain.
A characterization of the -realcompact space
A characterization of the invertible measures
Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
A characterization of weakly amenable Banach algebras
A cheaper Swiss cheese
A class of weighted composition operators on
A class of weighted convolution Fréchet algebras
For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists m ∈ ℕ such that...
A commutativity theorem for Banach algebras
A comparison between the closed modular ideals in l...(w) and L...(w).
A constructive proof of the Beurling-Rudin theorem
A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A(𝔻) is given.
A corrected correction
A counterexample in harmonic analysis