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Lower bounds for norms of products of polynomials on L p spaces

Daniel Carando;  Damián Pinasco;  Jorge Tomás Rodríguez — 2013

Studia Mathematica

For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on L p ( μ ) , whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes p . For p > 2 we present some estimates on the constants involved.

Lagrange approximation in Banach spaces

Lisa Nilsson;  Damián Pinasco;  Ignacio M. Zalduendo — 2015

Czechoslovak Mathematical Journal

Starting from Lagrange interpolation of the exponential function e z in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space E . Given such a representable entire funtion f : E → ℂ , in order to study the approximation problem and the uniform convergence of these polynomials to f on bounded sets of E , we present a sufficient growth condition on the interpolating...

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