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The group algebra of a locally compact group [PDF]
Transactions of the American Mathematical Society, 1947 Introduction. This paper concerns the theory of ideals in the algebra (called the group algebra) of all complex-valued functions on a locally compact (abbreviated to LC) group which are integrable with respect to Haar measure, multiplication being ...
I. Segal
semanticscholar +4 more sources
The weights of closed subgroups of a locally compact group [PDF]
, 2012 . Let G be an infinite locally compact group and let be a cardinal satisfying for the weight of G. It is shown that there is a closed subgroup N of G with .
S. Hernández, K. Hofmann, S. Morris
semanticscholar +5 more sources
The nub of an automorphism of a totally disconnected, locally compact group [PDF]
Ergodic Theory and Dynamical Systems, 2011 To any automorphism, $\alpha $, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha $-stable subgroup of $G$, here called the nub of $\alpha $, on which the action of $\alpha $ is ergodic.
G. Willis
semanticscholar +3 more sources
Exactness of locally compact groups
Advances in Mathematics, 2017 We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a compact Hausdorff ...
Adams +40 more
core +5 more sources
A dichotomy property for locally compact groups [PDF]
Journal of Functional Analysis, 2018 We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of $l_1$. For that purpose, we transfer to general locally compact groups the notion of interpolation ($I_0$) set, which was defined by ...
Ferrer, Marita +2 more
core +6 more sources
Pro-Lie Groups: A Survey with Open Problems
Axioms, 2015 A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete ...
Karl H. Hofmann, Sidney A. Morris
doaj +4 more sources
Compactness in Wiener amalgams on locally compact groups [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group.
S. S. Pandey
doaj +3 more sources
On unconditionally convergent series in topological rings
Karpatsʹkì Matematičnì Publìkacìï, 2022 We define a topological ring $R$ to be Hirsch, if for any unconditionally convergent series $\sum_{n\in\omega} x_i$ in $R$ and any neighborhood $U$ of the additive identity $0$ of $R$ there exists a neighborhood $V\subseteq R$ of $0$ such that $\sum_{n ...
T.O. Banakh, A.V. Ravsky
doaj +1 more source
Convolution Product for Hilbert $C^*$-Module Valued Maps [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we introduce a convolution-type product for strongly integrable Hilbert $C^*$-module valued maps on locally compact groups. We investigate various properties of this product related to uniform continuity, boundless, etc.
Mawoussi Todjro, Yaogan Mensah
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VARIABLE LEBESGUE ALGEBRA ON A LOCALLY COMPACT GROUP
Проблемы анализа, 2023 For a locally compact group 𝐻 with a left Haar measure, we study the variable Lebesgue algebra L^(p(.))(𝐻) with respect to convolution. We show that if L^(p(.))(𝐻) has a bounded exponent, then it contains a left approximate identity.
P. Saha, B. Hazarika
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