2014/10/16 by Michael Ćwikel, Richard Rochberg, Cwikel, Michael +1
Mathematics · #46B50. Secondary 46E15 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 46B70
paper · pdf · doi:10.48550/arxiv.1410.4527
openalex publication_date 2014/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It contains almost no new results. This time we discuss Nigel's partial solutions (obtained jointly with one of us) of the problem of whether the complex method of interpolation preserves the compactness of operators. This problem is now 51 years old and still lacks a complete solution. We also survey some other partial solutions of this problem, obtained before and after the above mentioned joint work. We are simultaneously posting a preliminary version of a technical sequel to this paper, which contains some small new results. Its future more elaborate version will probably conclude this series devoted to Nigel's research.