PreprintarXiv licencearXiv
Every compact operator is a commutator of compact operators
Abstract
We prove that every compact operator T on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors A and B can be chosen such that [A, B] = T and max{‖A‖,‖B‖}≤ c‖T‖1/2 for a universal constant c.
Related
- Divergence of decreasing rearranged Fourier series on every infinite compact abelian group
- Every Compact Metric Space Is Isometrically Embeddable into the Gromov-Hausdorff Space
- Spectral theorem for compact self-adjoint operators on smooth Banach spaces
- Hyponormal Toeplitz operators with operator valued normal symbols
- Compact linear combination of composition operators on weighted Bergman-Orlicz spaces induced by doubling weights
BibTeX
@misc{liu2026every,
title = {{Every compact operator is a commutator of compact operators}},
author = {Zhichao Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20672},
eprint = {2609.20672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20672},
}
RIS
TY - UNPB
TI - Every compact operator is a commutator of compact operators
AU - Zhichao Liu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.20672
UR - https://arxiv.org/abs/2609.20672
AB - We prove that every compact operator T on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors A and B can be chosen such that [A, B] = T and max{‖A‖,‖B‖}≤ c‖T‖^1/2 for a universal constant c.
ER -