G�rding domain and entire vectors for inductive limits of commutative locally compact groups

1984 ◽  
Vol 35 (4) ◽  
pp. 366-372 ◽  
Author(s):  
A. V. Kosyak ◽  
Yu. S. Samoilenko
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Inductive Limits ◽  
Locally Compact

Studies in harmonic analysis

1964 ◽  
Vol 60 (3) ◽  
pp. 465-516 ◽  
Author(s):  
N. Th. Varopoulos
Keyword(s):  
Harmonic Analysis ◽  
Complete Characterization ◽  
Locally Compact Groups ◽  
Topological Spaces ◽  
Compact Groups ◽  
Measure Algebra ◽  
Topological Groups ◽  
Inductive Limits ◽  
Locally Compact ◽  
Character Group

In this paper we shall be mainly concerned with the following three apparently widely differing questions.(a) What are the possible group topologies on an Abelian group that have a given, fixed continuous character group?In developing our theory, we are very strongly motivated by the duality theory of linear topological spaces and in particular by Mackey's theorem of that theory. This important result gives a complete characterization of all locally convex topologies on a linear space that have a given, fixed, separating dual space. The analogue of Mackey's theorem for groups, together with related results, is examined in sections 1 and 2 of part 2 of the paper.(b) What are the properties of topological groups that are denumerable inductive limits of locally compact groups? (See section 1 of part 1 of the paper for definitions.)Our aim here is to extend results known for locally compact groups to this larger class of groups. The topological study of these groups is carried out in section 3 of part 1 of the paper and the really deep results about their characters are proved in section 5 of part 3 of the paper, as applications of the theory developed in that part of the paper, which is a type of harmonic analysis for these groups.(c) What are the properties of certain algebras of measures of a locally compact group G, that strictly contain L1(G), and share most of the pleasing properties of L1(G), that is, they do not have any of the pathological features of the full measure algebra M(G) such as the Wiener–Pitt phenomenon or asymmetry?

On the Lp-conjecture for locally compact groups

2007 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
F. Abtahi ◽  
R. Nasr-Isfahani ◽  
A. Rejali
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact

Ergodic actions of group extensions on von Neumann algebras

1989 ◽  
Vol 112 (1-2) ◽  
pp. 71-112
Author(s):  
Klaus Thomsen
Keyword(s):  
Fixed Point ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Fixed Point Algebra ◽  
Atomic Centre

SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.

Locally compact groups with permutable closed subgroups

2021 ◽  
Vol 390 ◽  
pp. 107894
Author(s):  
Wolfgang Herfort ◽  
Karl H. Hofmann ◽  
Francesco G. Russo
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact
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