We describe the computations of some intrinsic constants associated to an n-dimensional normed space V, namely the N -th “allometry” constants κ∞(V) := inf { ‖T‖ · ‖T ′‖, T : `∞ → V, T ′ : V → `∞, TT ′ = IdV } . These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our computations for some low-dimensional spaces such as sequenc...

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

Recent results on Dirichlet series ∑ n an 1 ns , s ∈ C, with coefficients an in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence coincides for Dirichlet series and for m-homogeneous Dirichlet polynomials. But a classical non-trivial fact due to Bohnenblust and Hille shows that if X is one dimensional, this maximal width heavily depends o...

We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K) −→ Y such that P (f) = S(f). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.

We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges. Kergin interpolation is a generalization of both Lagrange interpolation in the one dimensional case, and the Taylor polynomial in the case where all interpolation points coincide. In several vari...

In this paper we study the weighted Bergman-Orlicz spaces Aα. Among other properties we get that Aα is a Banach space with the Luxemburg norm. We show that the set of analytic polynomials is dense in Aα. We also study compactness and continuity of the composition operator on Aα. Mathematics Subject Classification: 46E30, 47B33