Multipliers of some Banach ideals and Wiener-Ditkin sets

Rok, strany: 2005, 237 - 248

Let $L_w¹ (G)$ be a Beurling (convolution) algebra on a locally compact abelian group $G$. A Banach algebra $(S_w (G),|·|_Sw)$ continuously embedded into $L_w¹(G)$ (we may assume for its norm that $|· |_1,w ≤ |· |_Sw$) is called a Segal algebra for $L_w¹ (G)$ if it is dense subalgebra of $L_w¹ (G)$, translation invariant, satisfying $|L_a f|_Sw≤ w(a)| f |_Sw$ for all $f \in S_w (G)$, $a \in G$, and that $y \mapsto L_y f$ is continuous from $G$ into $S_w (G)$. The aim of this paper is to study the properties of $S_w (G)$. In the second section we characterize the multipliers from $L_w¹ (G)$ to $S_w (G)$. We also discuss the tensor product factorization $S_w (G)\mathbin{\underline{\otimes}} V = V$, where $V$ is a Banach $L_w¹(G)$@-module. In the third section some applications are given. In section four we discuss the Wiener-Ditkin sets of $S_w (G)$ and show that they are the same as those of $L_w¹ (G)$.

ISO 690:

Gürkanli, A. 2005. Multipliers of some Banach ideals and Wiener-Ditkin sets. In Mathematica Slovaca, vol. 55, no.2, pp. 237-248. 0139-9918.

APA:

Gürkanli, A. (2005). Multipliers of some Banach ideals and Wiener-Ditkin sets. Mathematica Slovaca, 55(2), 237-248. 0139-9918.