Dominated bilinear forms and 2-homogeneous polynomials

Details Dominated bilinear forms and 2-homogeneous polynomials Dominated bilinear forms and 2-homogeneous polynomials

2009-05-13

arxiv.org/abs/0905.2079v2

Mathematics

Functional Analysis

8 pages

Scientific paper

The main goal of this note is to establish a connection between the cotype of the Banach space X and the parameters r for which every 2-homogeneous polynomial on X is r-dominated. Let cotX be the infimum of the cotypes assumed by X and (cotX)* be its conjugate. The main result of this note asserts that if cotX > 2, then for every 1<= r < (cotX)* there exists a non-r-dominated 2-homogeneous polynomial on X.

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