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Gelfand transform for a Boehmian space of analytic functions

V. Karunakaran, R. Angeline Chella Rajathi (2011)

Annales Polonici Mathematici

Let H ( ) denote the usual commutative Banach algebra of bounded analytic functions on the open unit disc of the finite complex plane, under Hadamard product of power series. We construct a Boehmian space which includes the Banach algebra A where A is the commutative Banach algebra with unit containing H ( ) . The Gelfand transform theory is extended to this setup along with the usual classical properties. The image is also a Boehmian space which includes the Banach algebra C(Δ) of continuous functions on...

Généralisation des algèbres de Beurling

Philippe Tchamitchian (1984)

Annales de l'institut Fourier

Cet article est consacré à l’étude des espaces A ω = L 2 ( R n ; ω ( x ) d x ) qui sont des algèbres de Banach. On démontre que les multiplicateurs ponctuels de A ω sont les fonctions qui appartiennent localement et uniformément à A ω si et seulement si A ω contient des fonctions à support compact.

Generalization of the topological algebra ( C b ( X ) , β )

Jorma Arhippainen, Jukka Kauppi (2009)

Studia Mathematica

We study subalgebras of C b ( X ) equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.

Generalized weak peripheral multiplicativity in algebras of Lipschitz functions

Antonio Jiménez-Vargas, Kristopher Lee, Aaron Luttman, Moisés Villegas-Vallecillos (2013)

Open Mathematics

Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all 𝕂 -valued Lipschitz functions on X - where 𝕂 is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that R a n π ( T 1 ( f ) T 2 ( g ) ) R a n π ( S 1 ( f ) S 2 ( g ) ) for all f, g ∈ Lip0(X),...

Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

Jean Ludwig, Lyudmila Turowska (2006)

Studia Mathematica

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...

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