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For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on , 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 . For p > 2 we present some estimates on the constants involved.
Starting from Lagrange interpolation of the exponential function 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 . Given such a representable entire funtion , in order to study the approximation problem and the uniform convergence of these polynomials to on bounded sets of , we present a sufficient growth condition on the interpolating...
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