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arXiv · 2609.27211

SOT-large subspaces of non-cyclic operators

N. G. Albuquerque·G. Araújo·L. Bernal-González·E. Demétrio Jr.·J. Seoane-Sepúlveda
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Abstract

In this paper, we consider the strong operator topology (SOT) on the space $\mathcal{L} (X)$ of continuous linear operators on an infinite-dimensional Fréchet space $X$. The existence of SOT-dense subspaces as well as of SOT-closed infinite-dimensional subspaces inside the family of all non-cyclic operators is established. Other classes of operators, such as non-dense range or non-injective operators, are also studied in this regard. Moreover, we prove for the sequence space $\ell_p$ $(0 < p < \infty)$ that the family of all non-cyclic members of $\mathcal{L}(\ell_p)$ contains an isometric copy of $\ell_p$.

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N. G. Albuquerque, G. Araújo, L. Bernal-González, E. Demétrio Jr., J. Seoane-Sepúlveda. 2026-09-23. SOT-large subspaces of non-cyclic operators. https://arxiv.org/abs/2609.27211

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