The Application Of Probabilistic Methods In Banach Algebra And Convolution In A Matrix Algebra Nature

In this paper,we use the probabilistic method to solve the problem when lp1lp2…lpn is not a Banach algebra under Schur product. Our results extended Tonge's results. We obtain estimates for the norm of the random multilinear form defined by A(ei,6j, …es) = aij…s, where the aij…s is uniformly bounded, independent, mean zero random variable. And we give a common condition under which lp1 lp2…lpn is not a Banach algebra under Schur product.In this paper, we obtain a class of infinite matrix convolution product algebras, and study its several elementary properties.