| Mathematics |
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| Random quadralinear forms and schur product on tensors |
| MA Zhi-hao, WANG Cheng, HOU Li-ying |
| Department of Mathematics, Zhejang University, Hangzhou 310027, China; Ningbo Institute of Technology, Zhejiang University, Ningbo 315104, China; Radio and TV University, Daqing 163311, China |
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Abstract In this work, we made progress on the problem that lr⊗lp⊗lq 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:lrM×lpN×lqK×lsH→C, defined by: A(ei, ej, ek, es)=aijks, where the (aijks)\'s are uniformly bounded, independent, mean zero random variables. We proved that under some conditions lr⊗lp⊗lq⊗ls is not a Banach algebra under schur product.
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Received: 13 January 2003
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