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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.3 P.350-352

http://doi.org/10.1631/jzus.2004.0350


Random quadralinear forms and schur product on tensors


Author(s):  MA Zhi-hao, WANG Cheng, HOU Li-ying

Affiliation(s):  Department of Mathematics, Zhejang University, Hangzhou 310027, China; more

Corresponding email(s):   mamitli@zju.edu.cn

Key Words:  Random tensors, Schur product, Banach algebra


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MA Zhi-hao, WANG Cheng, HOU Li-ying. Random quadralinear forms and schur product on tensors[J]. Journal of Zhejiang University Science A, 2004, 5(3): 350-352.

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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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Reference

[1] Almasri, I., Li, J.L., Tonge, A.M., 2000. Random trilinear forms and the schur multiplication of tensors.Internat.J. Math. and Sci.,23:69-76.

[2] Bennett, G., Goodman, V., Newman, C.M., 1975. Norms of random matrices.Pacific J. Math.,59:359-365.

[3] Bennett, G., 1977. Schur multipliers.Duke Math. J.,44:603-639.

[4] Mantero, A.M., Tonge, A.M., 1980. The schur multiplication in tensor algebras.Studia Math.,68(1):1-24.

[5] Varopoulos, N.T., 1974. On an inequality of von Neumann and an application of the Matric theory of tensor products to operators theory.J. Funct. Anal.,16:83-100.

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