We lift upper and lower estimates from linear functionals to n-homogeneous polynomials and using this result show that l ∞ is finitely represented in the space of n-homogeneous poly-nomials, n ≥ 2, for any infinite dimensional Banach space. Refinements are also given. The classical Dvoretsky spherical sections theorem [5,13] states that l 2 is finitely represented in any infinite dimensional Ba...

1. Introduction. Let (R") is the algebra Q1(Rn) of all real-valued functions of class C1. In other words, for every fEG1(Rn) there is a sequence {pn} of polynomials such that pn—*/ uniformly o...

The Jacobi polynomials induce a translation operator on function spaces on the interval [−1, 1]. For any homogeneous Banach space B w.r.t. this translation, we can study the according little and big Lipschitz spaces, lipB(λ) and LipB(λ), respectively. The big Lipschitz spaces are not homogeneous themselves. Therefore we introduce semihomogeneous Banach spaces w.r.t. Jacobi translation, of which...

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c. series, and analogously, th...