Related papers: From Parseval to Grothendieck and a little beyond,…

We survey connections of the Grothendieck inequality and its variants to combinatorial optimization and computational complexity.

The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved,…

This paper is around the topics I discussed in the lecture I gave at the Isaac Newton Institute in Cambridge, July 2009, in the Introductory Workshop. This paper can be read as a companion to my paper [Sa\"i di], where detailed proofs can…

There is a mathematical error in the first version of this paper. A new corrected version will be posted when the error is fixed, possibly with a modified title.

Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded…

This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

As part of the search for the value of the smallest upper bound of the best constant for the famous Grothendieck inequality, the so-called Grothendieck constant (a hard open problem - unsolved since 1953), we provide a further approach,…

In the spirit of Grothendieck's famous inequality from the theory of Banach spaces, we study a sequence of inequalities for the noncommutative Schwartz space, a Fr\'echet algebra of smooth operators. These hold in non-optimal form by a…

Probably the most famous of Grothendieck's contributions to Banach space theory is the result that he himself described as "the fundamental theorem in the metric theory of tensor products". That is now commonly referred to as…

Redheffer's inequality and its extensions are applied to study the behavior and estimates of the first eigenvalue of $p$-Laplacian with respect to $p$. Furthermore, a Redheffer-type inequality for the generalized trigonometric function is…

In a previous paper we have defined a second basis of the Grothendieck group of a split reductive group over a finite field. In this paper we extend this to the case of nonsplit special orthogonal groups.

In this paper we look at Grothendieck's work on classifying holomorphic bundles over the complex projective line. The paper is divided into $4$ parts. The first and second part we build up the necessary background to talk about vector…

This is part one of a series of papers. In this series of papers, we consider problems analogous to the Oppenheim conjecture from the viewpoint of prehomogeneous vector spaces.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

This note is a commentary on the model-theoretic interpretation of Grothendieck's double limit characterization of weak relative compactness.

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…

A full reflective subcategory E of a presheaf category [C*,Set] is the category of sheaves for a topology j on C if and only if the reflection preserves finite limits. Such an E is called a Grothendieck topos. More generally, one can…

We present here several versions of the Grothendieck inequality over the skew field of quaternions: The first one is the standard Grothendieck inequality for rectangular matrices, and two additional inequalities for self-adjoint matrices,…

We establish an analogue of the Grothendieck inequality where the rectangular matrix is replaced by a symmetric/Hermitian matrix and the bilinear form by a quadratic form. We call this the symmetric Grothendieck inequality; despite its…

This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.