On Pietsch measures for summing operators and dominated polynomials

Original · EN

We relate the injectivity of the canonical map from C(Bₑ') to Lₚ(μ), where μ is a regular Borel probability measure on the closed unit ball Bₑ' 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.