Entrywise Loewner Preservers on Min and Max Matrix Cones

[2608.15125] Entrywise Loewner Preservers on Min and Max Matrix Cones Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Functional Analysis arXiv:2608.15125 (math) [Submitted on 15 Aug 2026] Title: Entrywise Loewner Preservers on Min and Max Matrix Cones Authors: Wei Xie View a PDF of the paper titled Entrywise Loewner Preservers on Min and Max Matrix Cones, by Wei Xie View PDF HTML (experimental) Abstract: Let \[ A_{\min}(x)=\bigl(x_{\min(i,j)}\bigr)_{i,j=1}^n, \qquad A_{\max}(x)=\bigl(x_{\max(i,j)}\bigr)_{i,j=1}^n \] be the Min and Max matrices generated by a real sequence \(x=(x_1,\ldots,x_n)\). Using their classical cone parametrizations, we give exact characterizations of entrywise maps preserving positive semidefiniteness, total nonnegativity, Loewner order, and Loewner convexity. Our main results concern the Loewner this http URL assuming continuity or differentiability, entrywise Loewner-order preservation is equivalent to \(f\) being nondecreasing and convex. On the Min and Max cones, requiring the Loewner-convexity inequality on arbitrary pairs is rigid and forces \(f\) to be affine. Under the standard convention of restricting the inequality to Loewner-comparable pairs, the condition automatically forces \(f\in C^1([0,\infty))\) and is equivalent to convexity of both \(f\) and \(f'\). The analogous statement holds for Loewner concavity. In each case, the condition is already detected in dimension two. We also show that \(f:[0,\infty)\to\mathbb R\) preserves positive semidefiniteness entrywise on all positive semidefinite Min or Max matrices if and only if \(f\) is nonnegative and nondecreasing; the same condition characterizes total-nonnegativity preservation. Finally, we determine the power-function ranges and Loewner-order automorphisms, characterize the entrywise preservers of the strict Min and Max classes, and relate these strict cones to inverse \(M\)-matrices and oscillatory matrices. Subjects: Functional Analysis (math.FA) ; Rings and Algebras (math.RA) MSC classes: 15A18 (Primary) 15B48, 26A51 (Secondary) Cite as: arXiv:2608.15125 [math.FA] (or arXiv:2608.15125v1 [math.FA] for this version) https://doi.org/10.48550/arXiv.2608.15125 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Wei Xie [ view email ] [v1] Sat, 15 Aug 2026 08:58:07 UTC (16 KB) Full-text links: Access Paper: View a PDF of the paper titled Entrywise Loewner Preservers on Min and Max Matrix Cones, by Wei Xie View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2026-08 Change to browse by: math math.RA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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