--- _id: '7509' abstract: - lang: eng text: "In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s, p,q,s∈R,\r\nwhere A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0Advances in Mathematics. 2020;365. doi:10.1016/j.aim.2020.107053 apa: Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2020.107053 chicago: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics. Elsevier, 2020. https://doi.org/10.1016/j.aim.2020.107053. ieee: H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” Advances in Mathematics, vol. 365. Elsevier, 2020. ista: Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 365, 107053. mla: Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” Advances in Mathematics, vol. 365, 107053, Elsevier, 2020, doi:10.1016/j.aim.2020.107053. short: H. Zhang, Advances in Mathematics 365 (2020). date_created: 2020-02-23T21:43:50Z date_published: 2020-05-13T00:00:00Z date_updated: 2023-08-18T06:37:09Z day: '13' ddc: - '515' department: - _id: JaMa doi: 10.1016/j.aim.2020.107053 ec_funded: 1 external_id: arxiv: - '1811.01205' isi: - '000522798000001' intvolume: ' 365' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1811.01205 month: '05' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Advances in Mathematics publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 365 year: '2020' ...