scholarly journals A duality theorem for representable locally compact groups with compact commutator subgroup

1952 ◽  
Vol 4 (2) ◽  
pp. 115-121 ◽  
Author(s):  
Shuichi Takahashi
Keyword(s):  
Duality Theorem ◽  
Commutator Subgroup ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

scholarly journals The Fourier Algebra for Locally Compact Groupoids

2004 ◽  
Vol 56 (6) ◽  
pp. 1259-1289 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Duality Theorem ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Hilbert Modules ◽  
Locally Compact ◽  
Classical Duality ◽  
Special Case

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

scholarly journals A Universal Property of the Takahashi Quasi-Dual

1972 ◽  
Vol 24 (3) ◽  
pp. 530-536 ◽  
Author(s):  
Detlev Poguntke
Keyword(s):  
Topological Group ◽  
Compact Group ◽  
Duality Theorem ◽  
Commutator Subgroup ◽  
Continuous Homomorphism ◽  
Locally Compact Group ◽  
Compact Groups ◽  
Almost Periodic ◽  
Topological Groups ◽  
Locally Compact

Topological group always means Hausdorff topological group, homomorphism (isomorphism) between topological groups always means continuous homomorphism (homeomorphic isomorphism). For a topological group G, the topological commutator subgroup (the closure of the algebraic commutator subgroup) is denoted by G’. For each locally compact group G, Takahashi has constructed a locally compact group GT (called the Takahashi quasi-dual) and a homomorphism G → GT such that GT is maximally almost periodic, and GT’ is compact. The category of all locally compact groups with these two properties is denoted by [TAK]. Takahashi's duality theorem states that G → GT is an isomorphism if G ∊ [TAK].

Sign in / Sign up

Export Citation Format

Share Document