2020/04/14 by A. Jiménez-Vargas, Jiménez-Vargas, A., Fereshteh Sady +1
Mathematics · #46B04 #47B38 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2004.06472
openalex publication_date 2020/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 2-locality problem of diameter-preserving maps between C(X)-spaces is addressed in this paper. For any compact Hausdorff space X with at least three points, we give an example of a 2-local diameter-preserving map on C(X) which is not linear. However, we show that for first countable compact Hausdorff spaces X and Y, every 2-local diameter-preserving map from C(X) to C(Y) is linear and surjective up to constants in some sense. This yields the 2-algebraic reflexivity of isometries with respect to the diameter norms on the quotient spaces.