THE EXISTENCE OF NONZERO COMPACT RIGHT MULTIPLIERS AND ARENS REGULARITY OF WEIGHTED BANACH ALGEBRAS

被引：2

作者：

Mehdipour, Mohammad Javad ^{[1
]}

Moghimi, Gholam Reza ^{[2
]}

机构：

[1] Shiraz Univ Technol, Dept Math, Shiraz, Iran

[2] Payame Noor Univ, Dept Math, Tehran, Iran

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2022年 / 52卷 / 06期

关键词：

locally compact group; weight function; measure algebra; compact right multiplier; Arens regularity; 2ND; IDEAL;

D O I：

10.1216/rmj.2022.52.2101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let omega be a weight function on a locally compact group g and let M(g, omega)*0 be the subspace of M(g, omega)* consisting of all functionals that vanish at infinity. We first introduce an Arens product on (M(g, omega)*0)* under which it is a Banach algebra. We then show that the existence of a nonzero compact right multiplier on (M(g, omega)*0)* is equivalent to compactness of g. We also prove that if (M(g, omega )*0)* is Arens regular, then g is discrete.

引用

页码：2101 / 2112

页数：12

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