Distorting Mixed Tsirelson Spaces

1996/04/19 by George Androulakis, Edward Odell, Androulakis, George +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9604217

Abstract

Any regular mixed Tsirelson space T(θ_n,S_n)_\N for which (θ_n)/(θⁿ) → 0, where θ=lim_n θ_n^1/n, is shown to be arbitrarily distortable. Certain asymptotic ℓ₁ constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (S_α)_{α< ω1} is proved and an application is given to show that for every Banach space X with a basis (e_i), the two Δ-spectrums Δ(X) and Δ(X,(e_i)) coincide.

Citations

• Complexity of weakly null sequences
• The distortion problem

Cited by

• Proximity to ℓ₁ and Distortion in Asymptotic ℓ₁ Spaces

Related

• Modified mixed Tsirelson spaces
• More Mixed Tsirelson Spaces That Are Not Isomorphic To Their Modified Versions
• On certain equivalent norms on Tsirelson's space
• Quasiminimality in mixed Tsirelson spaces
• On total incomparability of mixed Tsirelson spaces