Displaying similar documents to “Homogeneous algebras on the circle. II. Multipliers, Ditkin conditions”

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that ℓ p , ( 1 ≤ p ≤ ∞ ) are Q algebras and that A n = ℨ L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α > 1 / 2 .

Interpolation of operators when the extreme spaces are L ∞

Jesús Bastero, Francisco Ruiz (1993)

Studia Mathematica

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Under some assumptions on the pair ( A 0 , B 0 ) , we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are L ∞ . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.

Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

Construction and analysis of some convolution algebras

Arne Beurling (1964)

Annales de l'institut Fourier

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À une famille Ω de fonctions positives ω sur un groupe G abélien localement compact, on associe l’ensemble A 2 des fonctions qui sont de carré sommable sur G par rapport à d x / ω ( x ) pour au moins un ω ∈ Ω . Sous certaines conditions simples, portant sur Ω , c’est une algèbre de convolution, contenue dans L 1 ( G ) . On étudie particulièrement le cas G = droite réelle, Ω = ensemble des fonctions paires, sommables, décroissantes sur ] 0 , ∞ [ . Une caractérisation explicite de A ˜ (ensemble des transformées de Fourier des f ∈ A )...

Approximate identities in Banach function algebras

H. G. Dales, A. Ülger (2015)

Studia Mathematica

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In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to...