相关论文: Matrix versions of some classical inequalities
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…
We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that…
We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known…
We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…
Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.
Multilinear trace restriction inequalities are obtained for Hardy's inequality. More generally, detailed development is given for new multilinear forms for Young's convolution inequality, and a new proof for the multilinear…
The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.
We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of…
We translate inequalities and conjectures for immanants and generalized matrix functions into inequalities in the L\"owner order. These have the form of trace polynomials and generalize the inequalities from [FH, J. Math. Phys. 62 (2021),…
We establish two inequalities in real inner product spaces. The first is a multiplicative strengthening of the classical Hornich-Hlawka inequality: for all vectors $x, y, z$ in a real inner product space $H$ \[ \|x\|\,\|y\| +…
By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…
Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work…