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Title: | Random Clarkson inequalities and LP version of Grothendieck' s inequality |
Authors: | Tonge, A |
Issue Date: | 1985 |
Publisher: | Brunel University |
Citation: | Maths Technical Papers (Brunel University). January 1985, pp 1-11 |
Series/Report no.: | ;TR/01/85 |
Abstract: | In a recent paper Kato [3] used the Littlewood matrices to generalise Clarkson's inequalities. Our first aim is to indicate how Kato's result can be deduced from a neglected version of the Hausdorff-Young inequality which was proved by Wells and Williams [11]. We next establish "random Clarkson inequalities".. These show that the expected behaviour of matrices whose coefficients are random ±1's is, as one might expect, the same as the behaviour that Kato observed in the Littlewood matrices. Finally we show how sharp LP versions of Grothendieck's inequality can be obtained by combining a Kato-like result with a theorem of Bennett [1]on Schur multipliers. |
URI: | http://bura.brunel.ac.uk/handle/2438/2597 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_01_85.pdf | 187.28 kB | Adobe PDF | View/Open |
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