PreprintCC BY-NC-ND 4.0arXiv
A Family of Completely PPT Maps
Abstract
Given α∈ ℝ and $ B_1,\ldots,B_q\in M_{m,n}$, consider the map Φ±α,B(X)=αtr(X) Im± ∑s=1qBsXBs* for all X∈ Mn. In this study, necessary and sufficient conditions on α and B1,…,Bq are given that guarantee Φα,B± is k-positive, k-copositive, and k-PPT, respectively. As application, known results about the map αtr(X)In± X are recovered. Furthermore, singular value inequalities associated with these positivity constraints are considered.
Related
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BibTeX
@misc{rosa2026family,
title = {{A Family of Completely PPT Maps}},
author = {Kennett L. Dela Rosa and Iana Angela C. Fajardo and Cedie B. Reyes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07260},
eprint = {2609.07260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07260},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Family of Completely PPT Maps
AU - Kennett L. Dela Rosa
AU - Iana Angela C. Fajardo
AU - Cedie B. Reyes
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07260
UR - https://arxiv.org/abs/2609.07260
AB - Given α∈ ℝ and $ B_1,\ldots,B_q\in M_{m,n}$, consider the map Φ^±_α,B(X)=αtr(X) I_m± ∑_s=1^qB_sXB_s^* for all X∈ M_n. In this study, necessary and sufficient conditions on α and B_1,…,B_q are given that guarantee Φ_α,B^± is k-positive, k-copositive, and k-PPT, respectively. As application, known results about the map αtr(X)I_n± X are recovered. Furthermore, singular value inequalities associated with these positivity constraints are considered.
ER -