On invertible nonnegative Hamiltonian operator matrices

Generalized Euclidean distance matrices

Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices (GDMs) that include EDMs. Each GDM is an entry-wise nonnegative matrix. A GDM is not symmetric unless it is an EDM. By some new techniques, we show that many significant results on Euclidean distance matrices can be extended to generalized Euclidean distance matrices. These contain results about eigenvalues, inverse, determinant, spectral radius, Moore-Penrose inverse and some majorizatio…

Normalized image of a vector by an infinite product of nonnegative matrices

A sofic measure is the image of a Markov probability measure by a continuous morphism, and can be represented by means of products of matrices $A_n$ that belong to a finite set of nonnegative matrices. To prove that the multifractal formalism holds for such a measure, it is necessary to know whenever the sequence $n\mapsto\frac{A_1\cdots A_nv}{\Vert A_1\cdots A_nv\Vert}$ converges when $v$ is a positive vector. We give a sufficient condition for this convergence, that we use for the study of one Bernoulli convolution.

正交换子的正平方零算子

Positive commutators of positive square-zero operators

本文研究了正平方零算子的正交换子问题，并扩展了非负矩阵非负秩的概念到无限维空间。

例外余正矩阵的构造

Construction of exceptional copositive matrices

本文通过自由概率方法构造所有尺寸≥5的例外余正矩阵，并证明在Frobenius内积下余正与完全正矩阵锥截面的体积半径比有与n无关的下界。

由非负矩阵的无限乘积对向量进行归一化

Normalized image of a vector by an infinite product of nonnegative matrices

本文研究非负矩阵无限乘积对向量的归一化收敛问题，提出一个比 Birkhoff 压缩方法更普适的充分条件，并将其应用于构造弱 Gibbs Bernoulli 卷积及阐明相关概念联系。

FLI和FRI上三角算子矩阵的可逆补全

Invertible completions of FLI and FRI upper triangular operator matrices

本文研究了上三角算子矩阵的Fredholm左可逆和Fredholm右可逆补全问题，并得到了相应的扰动结果，应用于Fredholm左右谱的“填洞”问题。

On Exponential Factorizations of Matrices over Banach Algebras

We study exponential factorization of invertible matrices over unital complex Banach algebras. In particular, we prove that every invertible matrix with entries in the algebra of holomorphic functions on a closed bordered Riemann surface can be written as a product of two exponents of matrices over this algebra. Our result extends similar results proved earlier in [KS] and [L] for $2\times 2$ matrices.

On the joint spectral radius of nonnegative matrices

We give an effective bound of the joint spectral radius $ρ(Σ)$ for a finite set $Σ$ of nonnegative matrices: For every $n$, \[ \sqrt[n]{\left(\frac{V}{UD}\right)^{D} \max_C \max_{i,j\in C} \max_{A_1,\dots,A_n\inΣ}(A_1\dots A_n)_{i,j}} \le ρ(Σ) \le \sqrt[n]{D \max_C \max_{i,j\in C} \max_{A_1,\dots,A_n\inΣ}(A_1\dots A_n)_{i,j}}, \] where $D\times D$ is the dimension of the matrices, $U,V$ are respectively the largest entry and the smallest entry over all the positive entries of the matrices in $Σ$, and $C$ is taken over all strongly connected components in the dependency graph. The dependency gr…

论无穷矩阵

On infinite matrices

该研究针对带基巴拿赫空间中可表示为无穷矩阵的有界线性算子，证明可逆算子存在逆范数一致有界的可逆有限维算子序列，且有限维方程解收敛于原无穷维算子方程解。