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<p>We study operators on the Kalton–Peck Banach space <i>Z</i><sub>2</sub> 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 <i>Z</i><sub>2</sub>, but the product of two of them is a compact operator. Among applications, we show that every copy of <i>Z</i><sub>2</sub> in <i>Z</i><sub>2</sub> is complemented, and each semi-Fredholm operator on <i>Z</i><sub>2</sub> has complemented kernel and range, the space <i>Z</i><sub>2</sub> is <i>Z</i><sub>2</sub>-automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schechtman about strictly singular perturbations of operators on <i>Z</i><sub>2</sub>.</p>

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Operators on the Kalton–Peck space Z2

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月3日

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  • Jesús M. F. Castillo,
  • Manuel González,
  • Raúl Pino

摘要

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 Schechtman about strictly singular perturbations of operators on Z2.