In this work, we made progress on the problem that l_r directX l_p directX l_q 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 l_r directX l_p directX l_q directX l_s is not a Banach algebra under schur product.
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机译:在这项工作中,我们在l_r directX l_p directX l_q是schur乘积下的Banach代数的问题上取得了进展。我们的结果扩展了Tonge的结果。我们还获得了随机四线性形式A的范数的估计值:l_r〜M x l_p〜N x l_q〜K x l_s〜H→C,定义为:A(e_i,e_j,e_k,e_s)= a_(ijks) ,其中(a_(ijks))是一致有界的,独立的,均值为零的随机变量。我们证明了在某些情况下,在schur乘积下,l_r directX l_p directX l_q directX ls并不是Banach代数。
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