Search results for "Unconditional basis"

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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
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Estimates for the first and second Bohr radii of Reinhardt domains

2004

AbstractWe obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in Cn.

Power seriesMathematics(all)Numerical AnalysisMathematics::Complex VariablesUnconditional basisGeneral MathematicsApplied MathematicsMathematical analysisBanach spacePower seriesPolynomialsBohr modelsymbols.namesakeBanach spacesBohr radiiBounded functionSeveral complex variablessymbolsSeveral complex variablesAnalysisMathematicsJournal of Approximation Theory
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