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Operators Admitting a Closed Subspace of Cyclic Vectors

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Abstract

For an operator T acting on a complex infinite dimensional Banach space X such that \(T\oplus T\) is cyclic on \(X\oplus X\), we show that T admits a closed infinite dimensional subspace of cyclic vectors (excluding \(\{0\}\)). We give some applications of this result, and we show several examples of cyclic operators T with \(T\oplus T\) non-cyclic admitting a closed infinite dimensional subspace of cyclic vectors.

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Authors and Affiliations

  1. Department of Mathematics, University of Cantabria, Avenida de los Castros s/n, 39071, Santander, Spain

    Manuel González

  2. Department of Mathematics, University of Cádiz, Avenida de la Universidad s/n, 11405, Jerez de la Frontera, Spain

    Fernando León-Saavedra & Pilar Romero-de la Rosa

Authors
  1. Manuel González
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  2. Fernando León-Saavedra
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  3. Pilar Romero-de la Rosa
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Corresponding author

Correspondence to Fernando León-Saavedra.

Additional information

The first author was supported in part by Project MTM2016-76958, Spain.

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González, M., León-Saavedra, F. & Romero-de la Rosa, P. Operators Admitting a Closed Subspace of Cyclic Vectors. Integr. Equ. Oper. Theory 90, 28 (2018). https://doi.org/10.1007/s00020-018-2458-2

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  • DOI: https://doi.org/10.1007/s00020-018-2458-2

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