2-Co-lacunary sequences in noncommutative symmetric Banach spaces

TL;DR

This paper characterizes noncommutative symmetric Banach spaces where every bounded sequence contains either a convergent or a 2-co-lacunary subsequence, extending classical results to the noncommutative setting.

Contribution

It extends R"abiger's classical characterization to noncommutative symmetric Banach spaces, identifying conditions for subsequence structures.

Findings

Characterization of noncommutative symmetric Banach spaces with subsequence properties

Extension of classical results to noncommutative frameworks

Identification of conditions for 2-co-lacunary subsequences

Abstract

We characterize noncommutative symmetric Banach spaces for which every bounded sequence admits either a convergent subsequence, or a $2$-co-lacunary subsequence. This extends the classical characterization, due to R\"abiger.