Invertibility of matrix type operators of infinite order with exponential off-diagonal decay

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 …

希尔伯特空间上算子矩阵的可逆性性质

Invertibility properties of operator matrices on Hilbert spaces

本文针对希尔伯特空间上对角元已知的$n$维上三角算子矩阵$T_n^d(A)$，给出其各类Fredholm和Weyl补全的充要条件，修正前人结果并推广方法至任意$n\geq2$。

上三角算子矩阵及其各种谱的稳定性

Upper triangular operator matrices and stability of their various spectra

本文研究了上三角算子矩阵的各类谱稳定性，提供了不同可逆性类型的特征化及稳定性条件，推广了前人结果并完善了相关理论体系。

各类广义函数空间上伪微分算子的近乎对角化

Almost diagonalization of $Ψ$DO's over various generalized function spaces

研究以次指数与超指数增长的归纳、投影序列空间及调制空间极限为框架，建立伪微分算子的近乎对角化理论，并综述 Hörmander 度量下的相关结果。

扰动算子$T_n^d(A)$的谱

Perturbing the spectrum of operator $T_n^d(A)$

本文针对部分上三角算子矩阵$T_n^d(A)$，仅通过对角元刻画其（左、右）可逆性，推广并修正了相关前人结果，且在不假设可分性条件下给出n维类似物，还恢复或得到了其他学者的若干扰动结果。

Subsymmetric bases have the factorization property

We show that every subsymmetric Schauder basis $(e_j)$ of a Banach space $X$ has the factorization property, i.e. $I_X$ factors through every bounded operator $T\colon X\to X$ with a $δ$-large diagonal (that is $\inf_j |\langle Te_j, e_j^*\rangle| \geq δ> 0$, where the $(e_j^*)$ are the biorthogonal functionals to $(e_j)$). Even if $X$ is a non-separable dual space with a subsymmetric weak$^*$ Schauder basis $(e_j)$, we prove that if $(e_j)$ is non-$\ell^1$-splicing (there is no disjointly supported $\ell^1$-sequence in $X$), then $(e_j)$ has the factorization property. The same is true for $\…