Related papers: Golden-Thompson from Davis
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…
We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over…
In this paper we establish mixed weak inequalities of Fefferman-Stein type for Calder\'on-Zygmund operators and their commutators, improving some previous results known in the literature. The main estimates also generalize the classical…
We shall give a refinement of the arithmetic-geometric mean inequality.
We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…
We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.
The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.
We state and prove a version of Dyson's Lemma for a product of smooth projective varieties of arbitrary dimension using positivity methods.
Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
We present a short and self-contained proof of the choosability version of Brooks' theorem.
In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.
We derive a relative version of the slicing Bennequin inequalities for cobordant Legendrian knots, and review a few proofs of the result.
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the…
We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the…
We give a short proof of a recent inequality of Audenaert, Datta and Ozols, and determine cases of equality.
We prove several trace inequalities that extend the Araki Lieb Thirring (ALT) inequality, Golden Thompson (GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as…
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.