Related papers: Moore-Penrose inverse and partial orders on Hilber…
In this paper, the problems of perturbation and expression for the Moore--Penrose metric generalized inverses of bounded linear operators on Banach spaces are further studied. By means of certain geometric assumptions of Banach spaces, we…
Let $H_1,H_2$ be complex Hilbert spaces and $T:H_1\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\subseteq H_1$ and $T^{\dagger}$ be the Moore-Penrose inverse of $T$. Let $S:H_1\rightarrow H_2$ be a bounded operator.…
Let $t$ be a regular operator between Hilbert $C^*$-modules and $t^\dag$ be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator $t^*t$. More precisely, we study some conditions ensuring that…
In this paper, we present some interesting results to characterize the Moore-Penrose inverses of unbounded closable operators and the Cartesian product of closed operators in Hilbert spaces.
Let $\mathcal{R}$ be a unital ring with involution. The notions of 1MP-inverse and MP1-inverse are extended from $M_{m,n}(\mathbb{C)}$, the set of all $m\times n $ matrices over $\mathbb{C}$, to the set $\mathcal{R}% ^{\dagger}$ of all…
In this paper we derive necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of unbounded Gram operators between real Hilbert spaces. These conditions include statements on acuteness of certain closed convex…
We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization…
In the general setting of the adjointable operators on Hilbert $C^*$-modules, this paper deals mainly with the weighted Moore-Penrose (briefly weighted M-P) inverse $A^\dag_{MN}$ in the case that the weights $M$ and $N$ are self-adjoint…
For two positive definite adjointable operators $M$ and $N$, and an adjointable operator $A$ acting on a Hilbert $C^*$-module, some properties of the weighted Moore-Penrose inverse $A^\dag_{MN}$ are established. When $A=(A_{ij})$ is…
In this article properties of the $(b, c)$-inverse, the inverse along an element, the outer inverse with prescribed range and null space $A^{(2)}_{T, S}$ and the Moore-Penrose inverse will be studied in the contexts of Banach spaces…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
Every bounded linear operator on a Hilbert space which is invertible modulo compact operators has a closed range and is, thus, generalized invertible. We consider the analogue question in general $C^*$-algebras and describe the closed…
A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators.
The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…
In this paper, we establish a link between the Hyers-Ulam stability and the Moore--Penrose inverse, that is, a closed operator has the Hyers-Ulam stability if and only if it has a bounded Moore-Penrose inverse. Meanwhile, the stability…
Let $R$ be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary $*$-ring case. It is shown that the group, Moore-Penrose, core and dual core inverse are closely…
A Krein space H and bounded linear operators B, C on H are given. Then, some min and max problems about the operators (BX - C)^{#}(BX -C), where X runs over the space of all bounded linear operators on H, are discussed. In each case, a…
In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in which reverse order law holds good. Rank equivalence…
We give a constructive characterization of matrices satisfying the reverse-order law for the Moore--Penrose pseudoinverse. In particular, for a given matrix $A$ we construct another matrix $B$, of arbitrary compatible size and chosen rank,…