ﻻ يوجد ملخص باللغة العربية
Let $H$ be a compact subgroup of a locally compact group $G$ and let $m$ be the normalized $G$-invariant measure on homogeneous space $G/H$ associated with Weils formula. Let $varphi$ be a Young function satisfying $Delta_2$-condition. We introduce the notion of left module action of $L^1(G/H, m)$ on the Orlicz spaces $L^varphi(G/H, m).$ We also introduce a Banach left $L^1(G/H, m)$-submodule of $L^varphi(G/H, m).$
It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups are discussed as far as they carry.
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normali
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently the vector m
We prove the classical Hausdorff-Young inequality for Orlicz spaces on compact homogeneous manifolds.
We show that there is a one-to-one correspondence between compact quantum subgroups of a co-amenable locally compact quantum group $mathbb{G}$ and certain left invariant C*-subalgebras of $C_0(mathbb{G})$. We also prove that every compact quantum sub