TY - JOUR ID - 40584 TI - $n$-factorization Property of Bilinear Mappings JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Barootkoob, Sedigheh AD - Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran. Y1 - 2020 PY - 2020 VL - 17 IS - 3 SP - 161 EP - 173 KW - Bilinear map KW - Factorization property KW - Strongly Arens irregular KW - Automatically bounded and $w^*$-$w^*$-continuous DO - 10.22130/scma.2019.116000.696 N2 - In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:X\times Y\to Z$, 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. UR - https://scma.maragheh.ac.ir/article_40584.html L1 - https://scma.maragheh.ac.ir/article_40584_990c83bfc9f25fa8cb60df4af44b78d8.pdf ER -