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
收藏
页码：101 / 136
页数：36
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