Related papers: Golden-Thompson from Davis
For two hermitian matrices $A$ and $B$, Golden-Thompson inequality \cite{golden1965lower, thompson1965inequality} states that $$ \mathrm{tr}\left[ \exp{(A+B)} \right] \leq \mathrm{tr}\left[ \exp{(A)}\exp{(B)} \right]. $$ We elaborate here…
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
We prove some extensions of Andrews inequality.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
In this paper we give a simple proof of an inequality for intermediate Diophantine exponents obtained recently by W. M. Schmidt and L. Summerer.
The purpose of the paper is to present an short proof of the Chuang's inequality.
The purpose of this paper is to provide a random version of Simons' inequality.
Instantaneous derivation of the Thomas precession with only basic vector calculus.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
The Golden-Thompson inequality, ${\rm Tr} \, (e^{A + B}) \le {\rm Tr} \, (e^A e^B)$ for $A,B$ Hermitian matrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in…
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
We study concave trace functions of several operator variables and formulate and prove multivariate generalisations of the Golden-Thompson inequality. The obtained results imply that certain functionals in quantum statistical mechanics have…
In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized…
In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.
A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.