Search results for "Symmetric tensor product"

showing 2 items of 2 documents

Unconditional Basis and Gordon–Lewis Constants for Spaces of Polynomials

2001

Abstract No infinite dimensional Banach space X is known which has the property that for m ⩾2 the Banach space of all continuous m -homogeneous polynomials on X has an unconditional basis. Following a program originally initiated by Gordon and Lewis we study unconditionality in spaces of m -homogeneous polynomials and symmetric tensor products of order m in Banach spaces. We show that for each Banach space X which has a dual with an unconditional basis ( x * i ), the approximable (nuclear) m -homogeneous polynomials on X have an unconditional basis if and only if the monomial basis with respect to ( x * i ) is unconditional. Moreover, we determine an asymptotically correct estimate for the …

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsPolynomialBanach spacepolynomialBasis (linear algebra)Banach spaceMonomial basisunconditional basisUnconditional convergenceOrder (group theory)Interpolation spaceSymmetric tensorsymmetric tensor productGordon–Lewis propertyAnalysisMathematicsJournal of Functional Analysis
researchProduct

Pietsch's factorization theorem for dominated polynomials

2007

Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.

Discrete mathematicsPolynomialBanach spaceTensor product of Hilbert spacesDominated polynomialsAbsolutely summing linear operatorsSymmetric tensor productsymbols.namesakeSymmetric polynomialFactorization of polynomialsHomogeneous polynomialWeierstrass factorization theoremsymbolsElementary symmetric polynomialAnalysisMathematicsJournal of Functional Analysis
researchProduct