Compact and Weakly Compact Multipliers of Locally Compact Quantum Groups

被引：3

作者：

Medghalchi, Alireza ^{[1
]}

Mollakhalili, Ahmad ^{[1
]}

机构：

[1] Tarbiat Moallem Univ, Dept Math, Kharazmi Univ, 50 Taleghani Ave, Tehran 15618, Iran

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2018年 / 44卷 / 01期

关键词：

Locally compact quantum groups; (Weakly) compact operators; Amenability; Module homomorphims; 2ND CONJUGATE ALGEBRA; ARENS REGULARITY; MODULE HOMOMORPHISMS; FOURIER ALGEBRA; FINITE-DIMENSIONALITY; CHARACTER AMENABILITY; TOPOLOGICAL CENTERS; OPERATORS; SOCLE; PRODUCTS;

D O I：

10.1007/s41980-018-0008-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A locally compact group G is compact if and only if its convolution algebra has a non-zero (weakly) compact multiplier. Dually, G is discrete if and only if its Fourier algebra has a non-zero (weakly) compact multiplier. In addition, G is compact (respectively, amenable) if and only if the second dual of its convolution algebra equipped with the first Arens product has a non-zero (weakly) compact left (respectively, right) multiplier. We prove the non-commutative versions of these results in the case of locally compact quantum groups.

引用

页码：101 / 136

页数：36

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