98 citations · 979 across the 73 of their papers we have counts for
18 papers · 1 filter
Stability for the logarithmic Hardy-Littlewood-Sobolev Inequality with application to the Keller-Segel system
Eric A. Carlen
We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach t…
Monotonicity versions of Epstein's Concavity Theorem and related inequalities
Eric A. Carlen, Haonan Zhang
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 entrop…
A monotonicity version of a concavity theorem of Lieb
Eric A. Carlen
We give a simple proof of a strengthened version of a theorem of Lieb that played a key role in the proof of strong subadditivity of the quantum entropy.
On some convexity and monotonicity inequalities of Elliott Lieb
Eric A. Carlen
A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected…
Complete positivity and self-adjointness
Érik Amorim, Eric A. Carlen
We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family of inner products, also providing new…
On the convolution inequality
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb +1
We consider the inequality for real integrable functions on dimensional Euclidean space where denotes the convolution of with itself. We s…