%0 Journal Article
%T $n$-factorization Property of Bilinear Mappings
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Barootkoob, Sedigheh
%D 2020
%\ 07/01/2020
%V 17
%N 3
%P 161-173
%! $n$-factorization Property of Bilinear Mappings
%K Bilinear map
%K Factorization property
%K Strongly Arens irregular
%K Automatically bounded and $w^*$-$w^*$-continuous
%R 10.22130/scma.2019.116000.696
%X In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.
%U http://scma.maragheh.ac.ir/article_40584_cbae0f5dc8463173efac6e2a2c9b9cae.pdf