Random quadralinear forms and schur product on tensors.
In this work, we made progress on the problem that [ symbol: see text] is a Banach algebra under schur product. Our results extend Tonge's results. We also obtained estimates for the norm of the random quadralinear form A:l(r)(M) x l(p)(N) x l(q)(K) x l(s)(H)-->C, defined by: A(e(i), e(j), e(k), e(s))=a(ijks), where the (a(ijks))'s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions [ symbol: see text] is not a Banach algebra under schur product.
Ma
Zhi-Hao
ZH
Department of Mathematics, Zhejang University, Hangzhou 310027, China. mamitli@zju.edu.cn
Wang
Cheng
C
Hou
Li-Ying
LY
D000465:Algorithms; D016014:Linear Models; D015233:Models, Statistical; D013598:Systems Theory