Non-linear traces on matrix algebras, majorization, unitary invariant norms and 2-positivity

2021/09/05 by Masaru Nagisa, Nagisa, Masaru, Yasuo Watatani +1 · 2 citations
Computer Science · Mathematics · #46L07 (Primary) #47A64 (Secondary) #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L07 #msc:47A64

paper · pdf · doi:10.48550/arxiv.2109.02031

20 pages

arxiv created 2021/09/05 · openalex publication_date 2021/09/05 · arxiv updated 2021/09/07 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively. There exists a close relation among non-linear traces of Choquet type, majorization, unitary invariant norms and 2-positivity.

Citations

• Subalgebras of C*-algebras

Cited by

• Law of large numbers for non-linear traces of the Choquet type on finite factors
• Non-linear traces on the algebra of compact operators and majorization

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