arXiv subjects

Huanyin Chen

Publications and source records attributed to Huanyin Chen.

At least 19 recordsLinked to original sources

arXiv2026

Hybrid core-EP-$(b,c)$ inverses in rings

In this paper, we study when the core inverse in a ring coincides with its hybrid (b,c)-inverse, i.e., hybrid core-(b,c)-inverse. We present many characterizations of hybrid core-(b,c)-inverse. To establish a broader framework for this generalized inverses, we define hybrid core-EP-(b,c)-inverse that serves as a natural extension of the hybrid core-(b,c)-inverse. We characterize this new generalized inverse by combining the hybrid core-(b,c)-inverses and quasinilpotents. This generalized inverse is thereby examined through a novel limit-based approach. Its polar-like properties and image-based representations are presented.

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arXiv2026

Generalized EP properties of (b c) inverses

In this paper, we introduce the notion of the generalized (b,c) EP inverse within the framework of a *-Banach algebra. This concept emerges as a logical extension of the weak group inverse and EP-like property, which is applicable to complex matrices and bounded linear operators in Hilbert spaces. We provide its characterizations in relation to its associated decomposition and the generalized Drazin inverse. A polar-like property for the generalized (b,c) EP inverse is presented. Furthermore, we reveal an intrinsic connection between the generalized (b,b) EP inverse and the converse law for the generalized group inverse.

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arXiv2025

Generalized right group inverse in Banach *-algebras

In this paper, we introduce the concept of the generalized right group inverse within the context of a *-Banach algebra. This represents a natural extension of the generalized (weak) group inverse. Notably, this generalized inverse is characterized by integrating the right group inverse with the concept of quasinilpotency. We provide various characterizations and representations of the generalized right group inverse. Furthermore, we explore the relationship between the generalized right group inverse and the generalized right EP-inverse. The properties of the generalized (weak) group inverse in a Banach *-algebra are also extended to a more general framework.

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arXiv2025

The $m$-generalized right group inverses in Banach algebras

In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the m-generalized right group decomposition and a polar-like property. Additionally, we present the representation of the m-generalized right group inverse using the generalized right core inverse, leading to new insights and properties for both the m-weak group inverse and the generalized group inverse.

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arXiv2025

New properties of weighted generalized core-EP inverse in Banach algebras

We characterize the generalized weighted core-EP inverse via the canonical decomposition, utilizing a weighted core-EP invertible element and a quasinilpotent. We then offer a polar-like characterization for the generalized weighted core-EP invertible element. The representations of the generalized weighted core-EP inverse by leveraging the weighted generalized Drazin inverse are thereby presented. These lead to new properties for the weighted core-EP inverse.

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arXiv2024

m-weak group inverse in a ring with proper involution

The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and prove that it coincides with its m-weak group invertibility. We present the equivalent characterization of the m-weak group inverse by using a polar-like property. The relations between m-weak group inverse and core-EP inverse are also established. These give some new properties of the weak group inverse for complex matrices and ring elements.

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arXiv2024

Additive results of group inverses in Banach algebras

In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices is thereby obtained.

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arXiv2023

On generalized core-EP invertibility in a Banach algebra

We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for Banach *-algebra elements are thereby investigated. As applications, new properties of the core-EP inverse for block complex matrices are given.

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arXiv2023

The Sum of EP elements in a ring with involution

We present a necessary and sufficient conditions under which the sum of two EP elements in a *-ring has core inverse. As an application, we establish the conditions under which a block complex matrix with EP sub-blocks has core inverse.

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arXiv2023

G-Drazin inverse and group inverse for the anti-triangular block-operator matrices

We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let $E,F,EF^π\in \mathcal{B}(X)^d$. If $EFEF^π=0$ and $F^2EF^π=0$, we prove that $M=\left( \begin{array}{cc} E&I F&0 \end{array} \right)$ has g-Drazin inverse and its explicit representation is established. Moreover, necessary and sufficient conditions are given for the existence of the group inverse of $M$ under the condition $FEF^π=0$. The group inverse for the anti-triangular block-operator matrices with two identical subblocks is thereby investigated. These extend the results of Zhang and Mosić (Filomat, 32(2018), 5907--5917) and Zou, Chen and Mosić (Studia Scient. Math. Hungar., 54(2017), 489--508).

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arXiv2023

Hirano inverse of anti-triangular matrix over Banach Algebras

In this paper we investigate Hirano invertibility of anti-triangular matrix over a Banach algebra. Let $a\in {\mathcal A}^H, b\in {\mathcal A}^{sD}.$ If $b^Da=0, bab^π=0,$ we prove that $\begin{pmatrix} a&1\\ b&0 \end{pmatrix}\in M_2(\mathcal A)^H.$ Moreover, we considered Hirano invertibility of anti-triangular matrices under commutative-like conditions. These provide new kind of operator matrices with tripotent and nilpotent decompositions.

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arXiv2023

Study on Hirano Invertibility of Two New Types of Perturbed Operator Matrices

We investigate the Hirano invertibility of block-operator matrices in Banach algebras, and obtain the Hirano inverse of matrix $\begin{bmatrix} A&B\\ C&D \end{bmatrix}$ under two types of new perturbation conditions. Furthermore, we provide a new operator matrix decomposed into the sum of tripotent and nilpotent elements on Banach spaces.

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arXiv2022

The g-Drazin inverses of anti-triangular block operator matrices

An element $a$ in a Banach algebra $\mathcal{A}$ has g-Drazin inverse if there exists $b\in \mathcal{A}$ such that $ab=ba, b=bab$ and $a-a^2b \in \mathcal{A}^{qnil}$. In this paper we find new explicit representations of the g-Drazin inverse of the block operator matrix $\left( \begin{array}{cc} E&I F&0 \end{array} \right)$. We thereby solve a wider kind of singular differential equations posed by Campbell [S.L. Campbell, The Drazin inverse and systems of second order linear differential equations, Linear $\&$ Multilinear Algebra, 14(1983), 195--198].

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arXiv2022

The Core Inverse in a Banach Algebra with Involution

We present new additive results for the core inverse in a Banach algebra with involution. We obtain necessary and sufficient conditions under which the sum of two core invertible elements in a Banach algebra with involution is core invertible. Then we apply our results to block complex matrices and obtain certain conditions under which a block complex is core invertible. These generalize many known results, e.g.,~\cite[Theorem 4.3]{XCZ}, ~\cite[Theorem 2.5]{XS}.

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arXiv2022

Pseudo core invertibility in Banach *-algebras and its applications

We present new additive results for the pseudo core inverse in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two pseudo core invertible elements in Banach *-algebra is pseudo core invertible are obtained. As an application, the pseudo core invertibility for block complex matrices is investigated. These extend the main results of pseudo core invertibility of Gao and Chen [Comm. Algebra, 46(2018), 38--50].

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arXiv2022

Strongly Rad-clean Matrices over Commutative Local Rings

An element $a\in R$ is provided that there exists an idempotent $e\in R$ such that $a-e\in U(R), ae=ea$ and $eae\in J(eRe)$. In this article, we investigate strongly rad-clean matrices over a commutative local ring. We completely determine when a $2\times 2$ matrix over a commutative local ring is strongly rad-clean.

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arXiv2022

Group inverse for anti-triangular block operator matrices

We present the existence of the group inverse and its representation for the block operator matrix $\left( \begin{array}{cc} E&I\\ F&0 \end{array} \right)$ under the condition $FEF^π=0$. The group inverse for the anti-triangular block matrices with two identical subblocks under the same condition is thereby investigated. These extend the results of Zou, Chen and Mosić (Studia Scient. Math. Hungar., 54(2017), 489--508), and Cao, Zhang and Ge (J. Appl. Math. Comput., 46(2014), 169--179).

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arXiv2022

The g-Drazin invertibility in a Banach algebra

We present necessary and sufficient conditions under which the anti-triangular matrix $\left( \begin{array}{cc} a&b 1&0 \end{array} \right)$ over a Banach algebra has g-Drazin inverse. New additive results for g-Drazin inverse are obtained. Then we apply our results to $2\times 2$ operator matrices and generalize many known results, e.g.,~\cite[Theorem 2.2]{D}, ~\cite[Theorem 2.1]{YL} and \cite[Theorem 4.1]{Y}.

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