Conditional Bases with Property (A)

Constructive Approximation 2026 Open access

Read full text
Authors: Fernando Albiac, José Luis Ansorena, Miguel Berasategui, Pablo Manuel Berná
DOI: 10.1007/s00365-026-09747-6
Cited by: 1
References: 17

Abstract

Abstract Property (A) is a weak symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the study of the efficiency of the thresholding greedy algorithm in Banach spaces are sharp. In this note we build examples of Banach spaces with Schauder bases that have Property (A) but fail to be unconditional, thus settling a long standing problem in the area. As a by-product of our work we hone our construction to produce counterexamples that solve other open questions in the isometric theory of greedy bases.

Fields of Study & Subjects

Advanced Banach Space Theory Optimization and Variational Analysis Advanced Operator Algebra Research

Publication details

Journal / source
Constructive Approximation
Publisher
Springer Science and Business Media LLC
Volume
64
Issue
2
Pages
385-409
Publication date
31 March 2026
Language
EN