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arXiv · 2207.01069

Operators on the Kalton-Peck space $Z_2$

Jesús M. F. Castillo·Manuel González·Raúl Pino
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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 Schetchman about strictly singular perturbations of operators on $Z_2$.

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BibTeXRIS

Jesús M. F. Castillo, Manuel González, Raúl Pino. 2022-07-03. Operators on the Kalton-Peck space $Z_2$. https://arxiv.org/abs/2207.01069

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