MULTIPLIERS OF MULTIDIMENSIONAL FOURIER ALGEBRAS

作者：Todorov I G^*; Turowska L

来源：Operators and Matrices, 2010, 4(4): 459-484.

DOI：10.7153/oam-04-25

• Fourier algebra
• multiplier
• Schur multiplier
• multidimensional

Let G be a locally compact sigma-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra A(n)(G) of G. We characterise the completely bounded multidimensional multipliers associated with A(n)(G) in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all n-dimensional completely bounded multipliers into the space of all Schur multipliers on G(n+1) with respect to the (left) Haar measure. We show that in the case G is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of G introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

• 出版日期2010-12