Bases of random unconditional convergence in Banach spaces

TL;DR

This paper investigates the concept of random unconditional convergence in Banach space bases, exploring its relationship with classical unconditionality and examining properties like duality, reflexivity, and subsequences.

Contribution

It introduces new insights into the connections between random unconditional convergence and classical unconditionality, including duality and structural properties of bases.

Findings

Analyzes duality relations for random unconditional bases

Establishes conditions for reflexivity related to these bases

Demonstrates existence of unconditional subsequences in certain contexts

Abstract

We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases and existence of unconditional subsequences.