The reduced dual of a direct product of groups

1966 ◽  
Vol 62 (1) ◽  
pp. 5-6 ◽  
Author(s):  
Aubrey Wulfsohn
Keyword(s):  
Direct Product ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Type I ◽  
Locally Compact ◽  
Product Of Groups

AbstractIf one of the locally compact groups H and K is of type I, the reduced dual of their product is shown to be homeomorphic to the product of the reduced duals.

scholarly journals Ends of locally compact groups and their coset spaces

1974 ◽  
Vol 17 (3) ◽  
pp. 274-284 ◽  
Author(s):  
C. H. Houghton
Keyword(s):  
Compact Group ◽  
Direct Product ◽  
Compact Space ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Countable Base ◽  
Locally Compact ◽  
Coset Spaces ◽  
Compact Boundary

Freudenthal [5, 7] defined a compactification of a rim-compact space, that is, a space having a base of open sets with compact boundary. The additional points are called ends and Freudenthal showed that a connected locally compact non-compact group having a countable base has one or two ends. Later, Freudenthal [8], Zippin [16], and Iwasawa [11] showed that a connected locally compact group has two ends if and only if it is the direct product of a compact group and the reals.

scholarly journals Approximation property of C*-algebraic bundles

2002 ◽  
Vol 132 (3) ◽  
pp. 509-522 ◽  
Author(s):  
RUY EXEL ◽  
CHI-KEUNG NG
Keyword(s):  
Direct Product ◽  
Approximation Property ◽  
Discrete Case ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Discrete Groups ◽  
Locally Compact ◽  
Cross Sectional ◽  
The Cross

In this paper, we will define the reduced cross-sectional C*-algebras of C*-algebraic bundles over locally compact groups and show that if a C*-algebraic bundle has the approximation property (defined similarly as in the discrete case), then the full cross-sectional C*-algebra and the reduced one coincide. Moreover, if a semi-direct product bundle has the approximation property and the underlying C*-algebra is nuclear, then the cross-sectional C*-algebra is also nuclear. We will also compare the approximation property with the amenability of Anantharaman-Delaroche in the case of discrete groups.

The left Hilbert algebra associated to a semi-direct product

1977 ◽  
Vol 82 (3) ◽  
pp. 411-418 ◽  
Author(s):  
R. Rousseau
Keyword(s):  
Direct Product ◽  
Compact Support ◽  
Continuous Functions ◽  
Crossed Product ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Hilbert Algebra ◽  
Locally Compact ◽  
Continuous Action ◽  
Canonical Weight

AbstractLet A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".

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