Concavity of certain matrix trace and norm functions. II

@article{Hiai2012ConcavityOC,
  title={Concavity of certain matrix trace and norm functions. II},
  author={Fumio Hiai},
  journal={arXiv: Functional Analysis},
  year={2012}
}
  • F. Hiai
  • Published 28 October 2012
  • Mathematics
  • arXiv: Functional Analysis
Jointly convex mappings related to Lieb’s theorem and Minkowski type operator inequalities
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Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if $g(t)=\sum_{k=0}^m a_kt^k$ is a polynomial of degree $m$ with non-negative coefficients,
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
AbstractWe revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is $$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) =
On matrix inequalities between the power means: counterexamples
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
We consider the following trace function on n-tuples of positive operators: $${\Phi _P}({A_1},{A_2},...,{A_n}) = Tr({(\sum\limits_{j = 1}^n {A_j^P} )^{1/P}})$$ and prove that it is jointly
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This paper is concerned with certain convex or concave mappings of linear operators on a Hilbert space into the reals. [f(A) is convex if f(ilA + (1 il)B) <; t..j(A) + (1 il)f(B) for 0 < il < 1 and
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We consider a generalization of relative entropy derived from the Wigner–Yanase–Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint
CONCAVITY OF CERTAIN MATRIX TRACE FUNCTIONS
We demonstrate how Epstein's method using theory of Pick func-tions improves the existing results and also proves new ones on the joint con-cavity of trace functions of the form Tr (F(A1, . . .
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