In this paper, we investigate the perturbation for the Moore-Penrose inverse of closed operators on Hilbert spaces. By virtue of a new inner product defined on $H$, we give the expression of the Moore-Penrose inverse $\bar{T}^†$ and the upper bounds of
$\|\bar{T}^†\|$ and $\|\bar{T}^†-T^†\|$. These results obtained in this paper extend and improve many related results in this area.
In the present paper we investigate Moore-Penrose inverse and characteristic matrix of unbounded WCT operators on the Hilbert space $L^2(μ)$. Also, we obtain some applications of the Moore-Penrose inverse of unbounded operators on the Hilbert space $\mathcal{H}$ to variational regularization problem. Moreover,some examples are provided to illustrate the applications of our results in linear equations and specially Fredholm integral equations.
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 Löwner, star, minus, sharp and diamond orders. On the other hand, we analyze the validity of the reverse order law, $B^\dagger A^\dagger=(AB)^\dagger$, under hypothesis of operator ranges and also under hypothesis of order operators. Finally, we study the operator $B^\dagger A^\dagger$ as different weighted inverses of $AB$.
Effective partitioning method for computing weighted Moore-Penrose inverse
给出了多元多项式矩阵加权Moore-Penrose逆的一种计算方法和算法，并给出了适用于稀疏多项式矩阵的相关算法。这些方法和算法是[M. B. Tasic，P.S.斯塔尼米罗维奇，医学博士Petkovic，加权Moore-Penrose逆的分块法符号计算，应用数学计算。189（2007）615-640]中所描述的方法，以及这些算法在稀疏矩阵上的改进。这些方法也是[P. S. Stanimirovic，M.B.张文，有理矩阵与多项式矩阵的分块方法，应用数学与计算。155（2004）137-163;医学博士Petkovic，P.S. Stanimirovic，使用分区方法的Moore-Penrose逆的符号计算，Internat. J. Comput. Math. 82（2005）355-367]中的方法应用于加权Moore-Penrose逆的情况。算法在符号计算包MATHEMATICA中实现。
Antitonicity property of the Moore-Penrose inverse for selfadjoint operators
Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas, CIFASIS (CONICET-UNR)（中法阿根廷信息与系统科学国际中心，CIFASIS（CONICET-UNR））；Instituto Argentino de Matemática ‘‘Alberto P. Calderón’’, IAM-CONICET（阿尔贝托·P·卡尔德龙阿根廷数学研究所，IAM-CONICET）；Instituto de Ciencias, Universidad Nacional de General Sarmiento（通用萨米恩托国立大学科学院）
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 complete answer to the problem, including solvability conditions and characterization of the solutions, is presented. Also, an adequate decomposition of B is considered and the min-max problem is addressed. As a by-product the Moore-Penrose inverse of B is characterized as the only solution of a variational problem. Other generalized inverses are described in a …
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 theorem for a quadratic pencil of accretive operators. Also, we study a result of existence, uniqueness, and maximal regularity of the strict solution for complete abstract second order differential equation. Illustrative examples are also given.
We present more than 50 results including some range inclusion results to characterize reverse order law for Moore-Penrose inverse of closed range Hilbert space operators. We use basic properties of Moore-Penrose inverse to prove the results. Some examples are also provided to illustrate failure cases to hold the reverse order law in infinite dimensional settings.
Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces $H^s(\partial Ω)$ involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary $\partial Ω$ of a bounded Lipschitz domain $Ω\subset \mathbb R^d$ and applying Moore--Penrose pseudo-inverse properties together with a special inner product on $H^1(Ω)$. Moreover, generalized results of the Moore--Penrose pseudo-inverse are also established.
Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas, CIFASIS (CONICET-UNR)（中法阿根廷信息与系统科学国际中心，CIFASIS（CONICET-UNR））；Instituto Argentino de Matemática ‘‘Alberto P. Calderón’’, IAM-CONICET（阿根廷数学研究所“阿尔贝托·P·卡尔德隆”，IAM-CONICET）；Instituto de Ciencias, Universidad Nacional de General Sarmiento（科学学院，圣马丁国立大学）
Let $n$ be any natural number. The $n$-centered operator is introduced for adjointable operators on Hilbert $C^*$-modules. Based on the characterizations of the polar decomposition for the product of two adjointable operators, $n$-centered operators, centered operators as well as binormal operators are clarified, and some results known for the Hilbert space operators are improved. It is proved that for an adjointable operator $T$, if $T$ is Moore-Penrose invertible and is $n$-centered, then its Moore-Penrose inverse is also $n$-centered. A Hilbert space operator $T$ is constructed such that $T…
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 formulas with respect to IIPS are provided and an open problem is given at the end.
Fuglede-Putnam theorem is not true in general for $ EP $ operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for $ EP $ operators -- however proofs are totally different. Finally, interesting results on $ EP $ operators have been proved using several versions of Fuglede-Putnam type theorems for $ EP $ operators on Hilbert spaces.
Mosic and Djordjevic introduced the notation of the gDMP inverse for Hilbert space operators in [J. Spectr. Theory, 8(2):555-573, 2018] by considering generalized Drazin inverse with the Moore-Penrose inverse. This paper introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse for Hilbert space operators. The existence and uniqueness of the GD1 (also 1GD) inverse are discussed, along with some properties through core-quasinilpotent decomposition and closed range decomposition operator. We further establish a few explicit …
