Conditional quasi-greedy bases in non-superreflexive Banach spaces

2017/02/21 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +3
Mathematics · #41A65 #46B15 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1702.06326

openalex publication_date 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a conditional quasi-greedy basis B in a Banach space the associated conditionality constants k_m[B] verify the estimate k_m[B]=O(log m). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied whether this bound can be improved when we consider quasi-greedy bases in some special class of spaces. It is known that every quasi-greedy basis in a superreflexive Banach space verifies k_m[B]=(log m)^1-ε for some 0

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