ترغب بنشر مسار تعليمي؟ اضغط هنا

Ordered invariant ideals of Fourier-Stieltjes algebras

86   0   0.0 ( 0 )
 نشر من قبل John Quigg
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In a recent paper on exotic crossed products, we included a lemma concerning ideals of the Fourier-Stieltjes algebra. Buss, Echterhoff, and Willett have pointed out to us that our proof of this lemma contains an error. In fact, it remains an open question whether the lemma is true as stated. In this note we indicate how to contain the resulting damage. Our investigation of the above question leads us to define two properties emph{ordered} and emph{weakly ordered} for invariant ideals of Fourier-Stieltjes algebras, and we initiate a study of these properties.



قيم البحث

اقرأ أيضاً

70 - Nico Spronk 2018
We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G is connect ed, we show that operator amenability of B(G) entails that $G$ is compact.
146 - Hun Hee Lee , Xiao Xiong 2019
The Fourier(-Stieltjes) algebras on locally compact groups are important commutative Banach algebras in abstract harmonic analysis. In this paper we introduce a generalization of the above two algebras via twisting with respect to 2-cocycles on the g roup. We also define and investigate basic properties of the associated multiplier spaces with respect to a pair of 2-cocycles. We finally prove a twisted version of the result of Bo.{z}ejko/Losert/Ruan characterizing amenability of the underlying locally compact group through the comparison of the twisted Fourier-Stieltjes space with the associated multiplier spaces.
247 - Nico Spronk 2010
Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L^1(G) and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for L^1(G) and M(G). For us, ``amenability properties refers to amenability, weak amenability, and biflatness, as well as some properties which are more suited to special settings, such as the hyper-Tauberian property for semisimple commutative Banach algebras. We wish to emphasize that the theory of operator spaces and completely bounded maps plays an indispensable role when studying A(G) and B(G). We also show some applications of amenability theory to problems of complemented ideals and homomorphisms.
We examine the common null spaces of families of Herz-Schur multipliers and apply our results to study jointly harmonic operators and their relation with jointly harmonic functionals. We show how an annihilation formula obtained in J. Funct. Anal. 26 6 (2014), 6473-6500 can be used to give a short proof as well as a generalisation of a result of Neufang and Runde concerning harmonic operators with respect to a normalised positive definite function. We compare the two notions of support of an operator that have been studied in the literature and show how one can be expressed in terms of the other.
This paper is concerned with weak* closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak* closed subspaces of B(L^2(G)) which are invariant under both Schur multipliers and a canonical action of M(G) on B(L^2(G)) via completely bounded maps. We study the special cases of extremal ideals with a given null set and, for a large class of groups, we establish a link between relative spectral synthesis and relative operator synthesis.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا