2022/07/03 by Jesús M. F. Castillo, Castillo, Jesús M. F., Manuel González +3 · 1 citation
Mathematics · #46B03 #46B10 #46M18 #47A53 #47L20 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2207.01069
openalex publication_date 2022/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study operators on the Kalton-Peck Banach space Z2 from various points of view: matrix representations, examples, spectral properties and operator ideals. For example, we prove that there are non-compact, strictly singular operators acting on Z2, but the product of two of them is a compact operator. Among applications, we show that every copy of Z2 in Z2 is complemented, and each semi-Fredholm operator on Z2 has complemented kernel and range, the space Z2 is Z2-automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schetchman about strictly singular perturbations of operators on Z2.