Mathematical #Science: Some Elementary Inequalities

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Professor Bennett's project is mainly concerned with finding p,q - norm and lower bound estimates for linear transformations whose matrices have non-negative entries. The resulting inequalities are expected to have applications in numerous areas of analysis and probability theory. Mathematical analysis at the working level is often a matter of the ingenious manipulation of inequalities. For instance, there is a famous inequality asserting that the sum of products of two sequences of positive numbers is not greater than the square root of the sum of squares of the first sequence times the analogous expression for the second. This fact and countless others like it constitute the basic information out of which analytic arguments are spun. The research of Professor Bennett aims at fundamental enrichment of this store of facts.