On Pietsch measures for summing operators and dominated polynomials

Abstract

We relate the injectivity of the canonical map from $C(B_{E^{\prime }})$ to $L_p(\mu )$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E^{\prime }}$ of the dual $E^{\prime }$ 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 $\mu$ 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.

13 pages

References in corpus (1)

• Some new characterizations of Banach spaces containing ${\ell }^1$