Year: 2025
Type: article
Abstract: We study operators on the Kalton–Peck Banach space Z 2 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 Z 2 , but the product of two of them is a compact operator. Among applications, we show that every copy of Z 2 in Z 2 is complemented, and each semi-Fredholm operator on Z 2 has complemented kernel and range, the space Z 2 is Z 2 -automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schechtman about strictly singular perturbations of operators on Z 2 .
Source: Israel Journal of Mathematics
Institutions: Universidad de Extremadura, Universidad de Cantabria
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4409239384