اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRemarks on weak amenability of hypergroups
76
0
0.0
(
0
)
تأليف
Mahmood Alaghmandan
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the Cowling-Haagerup constant 1. As a corollary, we answer an open question of Eymard on Jacobi hypergroups. We also characterize the existence of bounded approximate identities for the hypergroup Fourier algebras of ultraspherical hypergroups.
قيم البحث
اقرأ أيضاً
Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also shown that a S
turm-Liouville hypergroup with a positive index is $alpha$-amenable if and only if $alpha=1$.
In this paper, we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context of locally compact hypergroups.
In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(Phi_1, Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $
fast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{Phi_1}(K)$ and $L^{Phi_2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^Phi_w(K)$ for a weight $w$ on a locally compact hypergroup $K$.
Associated to a nonzero homomorphism $varphi$ of a Banach algebra $A$, we regard special functionals, say $m_varphi$, on certain subspaces of $A^ast$ which provide equivalent statements to the existence of a bounded right approximate identity in the
corresponding maximal ideal in $A$. For instance, applying a fixed point theorem yields an equivalent statement to the existence of a $m_varphi$ on $A^ast$; and, in addition we expatiate the case that if a functional $m_varphi$ is unique, then $m_varphi$ belongs to the topological center of the bidual algebra $A^{astast}$. An example of a function algebra, surprisingly, contradicts a conjecture that a Banach algebra $A$ is amenable if $A$ is $varphi$-amenable in every character $varphi$ and if functionals $m_varphi$ associated to the characters $varphi$ are uniformly bounded. Aforementioned are also elaborated on the direct sum of two given Banach algebras.
We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $check{Delta}_G={(g,g^{-1}):gin G}$, is a s
et of local synthesis for $A(Gtimes G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected component of the identity $G_e$ is abelian.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
