Mathematical Sciences: Some Elementary Inequalities

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Professor Bennett will continue his research on "elementary inequalities," i.e. those involving matrices with non-negative entries. The main objective is to find norm estimates for various matrix transformations between sequence spaces. Applications are to probability theory, function theory, orthogonal series, and the general theory of inequalities. 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 constitutes the basic information out of which analytic arguments are spun. The research of Professor Bennett aims at fundamental enrichment of this store of facts.