相关论文: The g-Drazin inverses of anti-triangular block ope…

We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a…

Let $P(h),h\in]0,1]$ be a semiclassical scalar differential operator of order $2$. The existence of a supersymmetric structure given by a matrix $G(x;h)$ was exhibited in \cite{HeHiSj13} under rather general assumptions. In this note we…

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

We consider the relationship between derivations $d$ and $g$ of a Banach algebra $B$ that satisfy $\s(g(x)) \subseteq \s(d(x))$ for every $x\in B$, where $\s(\, . \,)$ stands for the spectrum. It turns out that in some basic situations, say…

We prove new spectral enclosures for the non-real spectrum of a class of $2\times2$ block operator matrices with self-adjoint operators $A$ and $D$ on the diagonal and operators $B$ and $-B^*$ as off-diagonal entries. One of our main…

Let $R$ be a ring with identity $1$. Jacobson's lemma states that for any $a,b\in R$, if $1-ab$ is invertible then so is $1-ba$. Jacobson's lemma has suitable analogues for several types of generalized inverses, e.g., Drazin inverse,…

In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…

In this article we explore several aspects concerning to the Moore-Penrose inverse of a bounded linear operator. On the one hand, we study monotonicity properties of the Moore-Penrose inverse with respect to the L\"owner, star, minus, sharp…

In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and…

We give a self-contained and simplified presentation of the theory of covariant representations for inverse semigroup actions on Banach algebras, which was recently introduced in the authors and A. Mckee in the twisted case. The main result…

We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) =…

Given an algebra with group $G$-action, we construct brace structures for its $G$-twisted Hochschild cochains. An an application, we construct $G$-Frobenius algebras for orbifold Landau-Ginzburg B-models and present explicit orbifold cup…

In this article we introduce several new examples of Wiener pairs $\mathcal{A} \subseteq \mathcal{B}$, where $\mathcal{B} = \mathcal{B}(\ell^2(X;\mathcal{H}))$ is the Banach algebra of bounded operators acting on the Hilbert space-valued…

Assume that $X$ is a complex separable infinite dimensional Banach space and $\mathcal{B}(X)$ denotes the Banach algebra of all bounded linear operators from $X$ to itself. In 1970, P.R. Halmos raised ten open problems in Hilbert spaces.…

The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite…

In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the…

In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…

We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…

The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational…