Jensen's inequality for operators and Loewner's theorem
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Publication:1158621
DOI10.1007/BF01450679zbMath0473.47011OpenAlexW1999983074MaRDI QIDQ1158621
Frank Hansen, Gert Kjaergård Pedersen
Publication date: 1982
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/163592
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Cites Work
