A MULTI-NORM STRUCTURE ON THE FOURIER AND FOURIER STIELTJES ALGEBRAS

Subject Areas : Statistics

Marzieh Shams Yousefi ¹ (Assistant Professor, Department of Puer Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.)

Received: 2018-08-28 Accepted : 2020-10-05 Published : 2021-05-22

Keywords: خاصیت تجزیه پذیری گروه های موضعا فشرده, واژگان کلیدی: فضا های نرم-چندگانه, جبرفوریه اشتیل یس, تجزیه متعامد, جبر فوریه,

Abstract :

In this paper, we introduce the decomposition property onlocally compact groups and we give a multi-norm structure based on the Fourier andFourier-Stieltjes algebras on locally compact groups with this property. We show that compact groups have the decomposition property. This construction generalizesthe known multi-norm structure of L1-algebras on compact abeliangroups. Also, we study some special multi-bounded maps on the Fourier algebrasand improve some results in this theory.*********************to avoid the web error I repeat the abstract*******************In this paper, we introduce the decomposition property onlocally compact groups and we give a multi-norm structure based on the Fourier andFourier-Stieltjes algebras on locally compact groups with this property. We show that compact groups have the decomposition property. This construction generalizesthe known multi-norm structure of L1-algebras on compact abeliangroups. Also, we study some special multi-bounded maps on the Fourier algebrasand improve some results in this theory.

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