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arXiv · 1210.3332

On Pietsch measures for summing operators and dominated polynomials

Geraldo Botelho·Daniel Pellegrino·Pilar Rueda
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Abstract

We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(μ)$, where $μ$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $μ$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.

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Geraldo Botelho, Daniel Pellegrino, Pilar Rueda. 2012-10-11. On Pietsch measures for summing operators and dominated polynomials. https://arxiv.org/abs/1210.3332

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