# Hlawka-Popoviciu inequalities on positive definite tensors

@article{Berndt2014HlawkaPopoviciuIO,
title={Hlawka-Popoviciu inequalities on positive definite tensors},
author={W Berndt and Suvrit Sra},
journal={arXiv: Functional Analysis},
year={2014}
}
• Published 1 November 2014
• Mathematics
• arXiv: Functional Analysis
9 Citations
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## References

SHOWING 1-10 OF 17 REFERENCES
Completely strong superadditivity of generalized matrix functions
• Mathematics
• 2014
We prove that generalized matrix functions satisfy a block-matrix strong superadditivity inequality over the cone of positive semidefinite matrices. Our result extends a recent result of
INEQUALITIES OF GENERALIZED MATRIX FUNCTIONS VIA TENSOR PRODUCTS
• Mathematics
• 2014
By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and
Positive Definite Matrices
• R. Bhatia
• Mathematics
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
• 2019
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real
Generalizations of Dobrushin's Inequalities and Applications
• Mathematics
• 1996
Abstract Letf: R n→ R be a seminorm and let (ei)1≤i≤nbe the canonical base of R n. DenoteM= 1 2 maxr, sf(er−es),K=maxrf(er). We prove the inequality f(x)\le
A determinantal inequality for positive semidefinite matrices
Let A, B, C be n A n positive semidefinite matrices. It is known that det(A + B + C) + det C â¥ det(A + C) + det(B + C), which includes det(A + B) â¥ det A + det B as a special case. In this
Induced operators on symmetry classes of tensors
• Mathematics
• 2001
Let V be an n-dimensional Hilbert space. Suppose H is a subgroup of the symmetric group of degree m, and X: H → C is a character of degree 1 on H. Consider the symmetrizer on the tensor space ⊗ m V
Hlawka’s functional inequality
AbstractThe paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) $$f(x+y)+f(y+z)+f(x+z)\leq f(x+y+z)+f(x)+f(y)+f(z)$$for the unknown mapping f defined on an
Multilinear Algebra
Theorem 1.1. Suppose that V , W are finite dimensional vector spaces over a field F . Then there exists a vector space T over F , and a bilinear map φ : V ×W → T such that T satisfies the following