正则、伪正则和几乎正则矩阵

On pseudo B-Weyl operators and generalized Drazin invertibility for operator matrices

We introduce a new class which generalizes the class of B-Weyl operators. We say that $T\in L(X)$ is pseudo B-Weyl if $T=T_1\oplus T_2$ where $T_1$ is a Weyl operator and $T_2$ is a quasi-nilpotent operator. We show that the corresponding pseudo B-Weyl spectrum $σ_{pBW}(T)$ satisfies the equality $σ_{pBW}(T)\cup[{\mathcal S}(T)\cap{\mathcal S}(T^*)]=σ_{gD}(T);$ where $σ_{gD}(T)$ is the generalized Drazin spectrum of $T\in L(X)$ and ${\mathcal S}(T)$ (resp., ${\mathcal S} (T^*)$) is the set where $T$ (resp., $T^*$) fails to have SVEP. We also investigate the generalized Drazin invertibility of …

Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

We study the global inversion of a continuous nonsmooth mapping $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f, introduced by Jeyakumar and Luc, and we consider a related index of regularity for f. We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard integral condition has a natural counterpart in this setting, providing a sufficient condition for global invertibility.

关于卷积权矩阵与正则性受控损失下的局部可解性

On convolved weight matrices and local solvability with controlled loss of regularity

本文引入抽象各向异性权矩阵的卷积，研究其性质，将其应用于Braun-Meise-Taylor权函数相关的各向同性矩阵，最终用于处理双曲型偏微分方程正则性受控损失下的局部可解性问题。

A characterization of $(\mathcal{I}, \mathcal{J})$-regular matrices

Let $\mathcal{I},\mathcal{J}$ be two ideals on $\mathbf{N}$ which contain the family $\mathrm{Fin}$ of finite sets. We provide necessary and sufficient conditions on the entries of an infinite real matrix $A=(a_{n,k})$ which maps $\mathcal{I}$-convergent bounded sequences into $\mathcal{J}$-convergent bounded sequences and preserves the corresponding ideal limits. The well-known characterization of regular matrices due to Silverman--Toeplitz corresponds to the case $\mathcal{I}=\mathcal{J}=\mathrm{Fin}$. Lastly, we provide some applications to permutation and diagonal matrices, which extend se…