Related papers: Majorization and arithmetic mean ideals
The objective of this note is to establish the Determinant Majorization Formula $F(A)^{1\over N} \geq \det(A)^{1\over n}$ for all operators $F$ determined by an invariant Garding-Dirichlet polynomial of degree $N$ on symmetric $n \times n$…
In this paper we continue to study the degrees of matrix coefficients of intertwining operators associated to reductive groups over $p$-adic local fields. Together with previous analysis of global normalizing factors we can control the…
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…
In [19] there is an approach to the investigation of the pseudocontinuability of Schur functions in terms of Schur parameters. In particular, there was obtained a criterion for the pseudocontinuability of Schur functions and the Schur…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional…
We consider infinitely dimensional classes of functions and instead of the relative error setting, which was used in previous papers on the integral norm discretization, we consider the absolute error setting. We demonstrate how known…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
Universal definitions of irredundance for X-set parameters are presented using blocking sets. This approach is modeled on (domination) irredundance (which uses closed neighborhoods as blocking sets) and zero forcing irredundance (which uses…
Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Greene--Skandera (2011), Sra (2016), Khare--Tao (2021),…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental…
We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solve the analogous…
The present work is devoted to an extension of the well-known Ehrling inequalities, which quantitatively characterize compact embeddings of function spaces, to more general operators. Firstly, a modified notion of continuity for linear…
Hindman's celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Menger's classic covering property. The methods…