From Matrix to Operator Inequalities
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Publication:2888788
DOI10.4153/CMB-2011-063-8zbMATH Open1245.46046arXiv0902.0102MaRDI QIDQ2888788
Publication date: 4 June 2012
Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)
Abstract: We generalize Loewner's method for proving that matrix monotone functions are operator monotone. The relation x leq y on bounded operators is our model for a definition for C*-relations of being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved, and verify a technical condition, then such a theorem will follow from its restriction to matrices. Applications are shown regarding norms of exponentials, the norms of commutators and "positive" noncommutative *-polynomials.
Full work available at URL: https://arxiv.org/abs/0902.0102
relationsorderbounded operatorsmatrices\(C^*\)-algebrasoperator normcommutatorexponentialresidually finite dimensional
Related Items (4)
Inequalities involving upper bounds for certain matrix operators ⋮ Title not available (Why is that?) ⋮ Operator-valued Extensions of Matrix-norm Inequalities ⋮ Estimating Norms of Commutators
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