Scalar-valued dominated polynomials on Banach spaces

Botelho, Geraldo; Pellegrino, Daniel

doi:10.1090/S0002-9939-05-08501-1

Scalar-valued dominated polynomials on Banach spaces
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by Geraldo Botelho and Daniel M. Pellegrino PDF

Proc. Amer. Math. Soc. 134 (2006), 1743-1751 Request permission

Abstract:

It is well known that 2-homogeneous polynomials on ${\mathcal L}_\infty$-spaces are 2-dominated. Motivated by the fact that related coincidence results are possible only for polynomials defined on symmetrically regular spaces, we investigate the situation in several classes of symmetrically regular spaces. We prove a number of non-coincidence results which makes us suspect that there is no infinite dimensional Banach space $E$ such that every scalar-valued homogeneous polynomial on $E$ is $r$-dominated for every $r \geq 1$.

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