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SOT-large subspaces of non-cyclic operators
Abstract
In this paper, we consider the strong operator topology (SOT) on the space 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 ℓp (0 < p < ∞) that the family of all non-cyclic members of ℒ(ℓp) contains an isometric copy of ℓp.
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BibTeX
@misc{albuquerque2026sotlarge,
title = {{SOT-large subspaces of non-cyclic operators}},
author = {N. G. Albuquerque and G. Araújo and L. Bernal-González and E. Demétrio Jr. and J. Seoane-Sepúlveda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27211},
eprint = {2609.27211},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27211},
}
RIS
TY - UNPB
TI - SOT-large subspaces of non-cyclic operators
AU - N. G. Albuquerque
AU - G. Araújo
AU - L. Bernal-González
AU - E. Demétrio Jr.
AU - J. Seoane-Sepúlveda
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27211
UR - https://arxiv.org/abs/2609.27211
AB - In this paper, we consider the strong operator topology (SOT) on the space 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 ℓ_p (0 < p < ∞) that the family of all non-cyclic members of ℒ(ℓ_p) contains an isometric copy of ℓ_p.
ER -