A quasimartingale characterization of p stable type Banach spaces

TL;DR

This paper characterizes Banach spaces of stable type p (1 < p < 2) through the quasimartingale property of normalized sums of independent, centered B-valued random variables under certain integrability conditions.

Contribution

It provides a new quasimartingale-based criterion for identifying Banach spaces of stable type p, extending existing characterizations.

Findings

Banach spaces of stable type p are characterized by quasimartingale behavior.

Normalized sums of B-valued random variables form quasimartingales in these spaces.

The result links probabilistic properties with geometric structure of Banach spaces.

Abstract

We characterize Banach spaces B of stable type p (1 < p < 2) by the property that for every sequence (X_i) of B-valued random variables, independent, centered and fulfilling some integrability assumption, the sequence S_n/n^(1/p) is a quasimartingale, where S_n=X_1+...+X_n.