Non-Linear Traces on Matrix Algebras, Majorization, Unitarily Invariant Norms and 2-Positivity

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 Ch...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2022-12, Vol.48 (4), p.1105-1126
Main Authors: Nagisa, M., Watatani, Y.
Format: Article
Language:English
Subjects:
Analysis
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Norms
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Summary: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, unitarily invariant norms and the 2-positivity.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-022-0179-x