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Order automorphisms of partial isometries in Mn(ℂ)
Abstract
We investigate and characterize order automorphisms on the set of partial isometries in the finite-dimensional matrix algebra Mn(ℂ). Different from the classical order automorphisms of subspace lattices, which can be implemented by standard invertible or unitary transformations, the order automorphisms considered herein admit no such conventional matrix representations. Instead, they are essentially governed by matrices such that I−(A+A*) is either positive or negative invertible. The results reveal that the structural features of order automorphisms for partial isometries are substantially more intricate than those of classical subspace automorphisms.
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BibTeX
@misc{jia2026order,
title = {{Order automorphisms of partial isometries in $M_n(\mathbb C)$}},
author = {Fengyang Jia and Guoxing Ji},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25559},
eprint = {2609.25559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25559},
}
RIS
TY - UNPB
TI - Order automorphisms of partial isometries in M_n(ℂ)
AU - Fengyang Jia
AU - Guoxing Ji
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25559
UR - https://arxiv.org/abs/2609.25559
AB - We investigate and characterize order automorphisms on the set of partial isometries in the finite-dimensional matrix algebra M_n(ℂ). Different from the classical order automorphisms of subspace lattices, which can be implemented by standard invertible or unitary transformations, the order automorphisms considered herein admit no such conventional matrix representations. Instead, they are essentially governed by matrices such that I−(A+A^*) is either positive or negative invertible. The results reveal that the structural features of order automorphisms for partial isometries are substantially more intricate than those of classical subspace automorphisms.
ER -