Work

Conditional Bases with Property (A)

Year: 2026

Type: article

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.

Source: Constructive Approximation

DOI: 10.1007/s00365-026-09747-6

Authors: Fernando Albiac, José L. Ansorena, Miguel Berasategui, Pablo M. Berná

Institutions: Universidad Pública de Navarra (UPNA), Universidad de La Rioja, Universidad de Buenos Aires, CUNEF Universidad

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción de la Investigación, el Desarrollo Tecnológico y la Innovación, Agencia Nacional de Promoción Científica y Tecnológica, Agencia Estatal de Investigación