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CLC number: O177.5; O211
On-line Access: 2024-08-27
Received: 2023-10-17
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Random quadralinear forms and schur product on tensors
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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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author="MA Zhi-hao, WANG Cheng, HOU Li-ying",
journal="Journal of Zhejiang University Science A",
volume="5",
number="3",
pages="350-352",
year="2004",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.0350"
}
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%A HOU Li-ying
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A1 - HOU Li-ying
J0 - Journal of Zhejiang University Science A
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%@ 1869-1951
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2004.0350
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.
[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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