6533b820fe1ef96bd12799ed
RESEARCH PRODUCT
On Pietsch measures for summing operators and dominated polynomials
Geraldo BotelhoDaniel PellegrinoPilar Ruedasubject
Unit sphereDiscrete mathematics28C15 46G25 47B10 47L22Mathematics::Functional AnalysisPure mathematicsAlgebra and Number TheoryDiscrete orthogonal polynomialsBanach spaceMeasure (mathematics)Functional Analysis (math.FA)Mathematics - Functional AnalysisClassical orthogonal polynomialsFactorizationOrthogonal polynomialsFOS: MathematicsCanonical mapMathematicsdescription
We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ 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 $\mu$ 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-10-11 | Linear and Multilinear Algebra |