Weakly null sequences with upper estimates

2007/05/02 by Freeman, Daniel
#46B03 #46B10 #46B20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0705.0218

Abstract

We prove that if (v_i) is a normalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by (v_i), then there exists a uniform constant C≥1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by (v_i). This extends a result of Knaust and Odell, who proved this for the cases in which (v_i) is the standard basis for ℓ_p or c₀.

Related

• Unconditional structures of weakly null sequences
• Weakly null sequences in the Banach space C(K)
• On Schreier unconditional sequences
• On Weakly Null FDD's in Banach Spaces
• A note on asymptotically monotone basic sequences and well-separated sets