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 $f:Xtimes Yto Z$, 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.
UR - http://scma.maragheh.ac.ir/article_40584.html
L1 - http://scma.maragheh.ac.ir/article_40584_cbae0f5dc8463173efac6e2a2c9b9cae.pdf
ER -