Group inverses and Drazin inverses over Banach algebras

Huang, Danrun

doi:10.1007/bf01322546

Cited by 7 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As is well known, A g exists if and only if rank A rank A 2 . The generalized inverses, and in particular Moore-Penrose, group and Drazin inverses, have also been studied in the context of semigroups, rings of Banach and C * algebras see 4-8 . In addition, if a matrix X satisfies 1 and 5 , then it is called a {1, 5}-inverse of A and is denoted by A 1,5 .…”

Section: Introductionmentioning

confidence: 99%

An Analog of the Adjugate Matrix for the Outer Inverse AT,S(2)

Liu

Zhu

Zhou

et al. 2012

Mathematical Problems in Engineering

View full text Add to dashboard Cite

We investigate the determinantal representation by exploiting the limiting expression for the generalized inverseAT,S(2). We show the equivalent relationship between the existence and limiting expression ofAT,S(2)and some limiting processes of matrices and deduce the new determinantal representations ofAT,S(2), based on some analog of the classical adjoint matrix. Using the analog of the classical adjoint matrix, we present Cramer rules for the restricted matrix equationAXB=D, R(X)⊂T, N(X)⊃S∼.

show abstract

Section: Introductionmentioning

confidence: 99%

An Analog of the Adjugate Matrix for the Outer Inverse AT,S(2)

Liu

Zhu

Zhou

et al. 2012

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Combining theorem 2.5 (or corollary 2.9) and theorem 3.1, we then get directly the following existence criteria and commuting relations for the classical inverses [4], [2], [5], [6], [7], [8], [14], [9]:…”

Section: Inverses Along D and Classical Inversesmentioning

confidence: 99%

“…There exist many specific generalized inverses in the literature, such as the group inverse, the Moore-Penrose inverse [1] or the Drazin inverse ( [2], [1]). Necessary and sufficient conditions for the existence of such inverses are known ([4], [2], [5], [6], [7], [8], [14], [9]), as are their properties. If one looks carefully at these results, it appears that these existence criteria all involve Green'relations [4], and that all inverses have double commuting properties.…”

mentioning

confidence: 99%