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|Title:||Random Clarkson inequalities and LP version of Grothendieck' s inequality|
|Citation:||Maths Technical Papers (Brunel University). January 1985, pp 1-11|
|Abstract:||In a recent paper Kato  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 . 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 on Schur multipliers.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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