@article{12216,
  abstract     = {Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.},
  author       = {Carlen, Eric A. and Zhang, Haonan},
  issn         = {0024-3795},
  journal      = {Linear Algebra and its Applications},
  keywords     = {Discrete Mathematics and Combinatorics, Geometry and Topology, Numerical Analysis, Algebra and Number Theory},
  pages        = {289--310},
  publisher    = {Elsevier},
  title        = {{Monotonicity versions of Epstein's concavity theorem and related inequalities}},
  doi          = {10.1016/j.laa.2022.09.001},
  volume       = {654},
  year         = {2022},
}

@article{8373,
  abstract     = {It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.},
  author       = {Pitrik, József and Virosztek, Daniel},
  issn         = {0024-3795},
  journal      = {Linear Algebra and its Applications},
  keywords     = {Kubo-Ando mean, weighted multivariate mean, barycenter},
  pages        = {203--217},
  publisher    = {Elsevier},
  title        = {{A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means}},
  doi          = {10.1016/j.laa.2020.09.007},
  volume       = {609},
  year         = {2021},
}