Convergence of the Rademacher series in a Banach space. (English) Zbl 0951.60009

Nguyen Duy Tien; Vidal Vazquez, Ricardo

Vietnam J. Math. 26, No. 1, 71-85 (1998).

Necessary and sufficient conditions for a.s. convergence of the series \(\sum r_nTe_n\), where \(T:H\to X\) is a linear continuous map from a Hilbert space \(H\) with an orthonormal basis \(\{e_n\}\) to a Banach space \(X\) and \(\{r_n\}\) is a Rademacher series, is given. Obviously, geometric language (cotype, containing of \(c_0\), etc.) is used.

Reviewer: Z.G.Gorgadze (Tbilisi)

MSC:

60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)
46B20	Geometry and structure of normed linear spaces

Keywords:

almost sure convergence; Banach space; Rademacher series; geometric language