In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R（?）C（?）H. Let H<sup>m×n</sup> denote the set of all m×n matrices over H.If A=(a<sub>rs<...Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R（?）C（?）H. Let H<sup>m×n</sup> denote the set of all m×n matrices over H.If A=(a<sub>rs</sub>)∈H<sup>m×n</sup>,then there exist A<sub>1</sub> and A<sub>2</sub>∈C<sup>m×n</sup> such that A=A<sub>1</sub>+A<sub>2</sub>j.Let A<sub>C</sub> denote the complexrepresentation of A,that is the 2m×2n complex matrix Ac=（（A<sub>1</sub>/A<sub>2</sub>）（-A<sub>2</sub>/A<sub>1</sub>））（see[1,2]）.We denote by A<sup>D</sup> the Drazin inverse of A∈H<sup>m×n</sup> which is the unique solution of the e-展开更多
Let A be a complex Banach algebra and J be the Jacobson radical of A.(1)We firstly show that a is generalized Drazin invertible in A if and only if a+J is generalized Drazin invertible in A/J.Then we prove that a is p...Let A be a complex Banach algebra and J be the Jacobson radical of A.(1)We firstly show that a is generalized Drazin invertible in A if and only if a+J is generalized Drazin invertible in A/J.Then we prove that a is pseudo Drazin invertible in si if and only if a+J is Drazin invertible in A/J.As its application,the pseudo Drazin invertibility of elements in a Banach algebra is explored.(2)The pseudo Drazin order is introduced in A.We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order,then we prove that the pseudo Drazin order is a pre-order.展开更多
For a Banach algebra A with identity and a, b, c, d ∈ A, the relations between the extended g-Drazin inverse(resp. generalized strong Drazin inverse)of ac and that of bd are given, when bac = bdb and cac = cdb.
In this paper,we give further results on the Drazin inverse of tensors via the Einstein product.We give a limit formula for the Drazin inverse of tensors.By using this formula,the representations for the Drazin invers...In this paper,we give further results on the Drazin inverse of tensors via the Einstein product.We give a limit formula for the Drazin inverse of tensors.By using this formula,the representations for the Drazin inverse of several block tensor are obtained.Further,we give the Drazin inverse of the sum of two tensors based on the representation for the Drazin inverse of,a block tensor.展开更多
For bounded linear operators A,B,C and D on a Banach space X,we show that if BAC=BDB and CDB=CAC then I-AC is generalized Drazin-Riesz invertible if and only if I-BD is generalized Drazin-Riesz invertible,which gives ...For bounded linear operators A,B,C and D on a Banach space X,we show that if BAC=BDB and CDB=CAC then I-AC is generalized Drazin-Riesz invertible if and only if I-BD is generalized Drazin-Riesz invertible,which gives a positive answer to Question 4.9 in Yan,Zeng and Zhu[Complex Anal.Oper.Theory 14,Paper No.12(2020)].In particular,we show that Jacobson’s lemma holds for generalized Drazin-Riesz inverses.展开更多
Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin inverti...Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.展开更多
This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin...This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.展开更多
Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is d...Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is defined byσ_(gD)(α)={λ∈C:α-λe is not generalized Drazin invertible}.It is shown thatσ_(gD)(a)∪σ_(gD)(b)=σ_(gD)(M_(C))∪W_(2),where W_(g) is a union of certain holes σ_(gD) and W_(g)■σ_(gD)(a)∩σ_(gD)(b),or more finely.In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.展开更多
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
基金Supported by the Natural Science Foundation of jiangxi
文摘Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R（?）C（?）H. Let H<sup>m×n</sup> denote the set of all m×n matrices over H.If A=(a<sub>rs</sub>)∈H<sup>m×n</sup>,then there exist A<sub>1</sub> and A<sub>2</sub>∈C<sup>m×n</sup> such that A=A<sub>1</sub>+A<sub>2</sub>j.Let A<sub>C</sub> denote the complexrepresentation of A,that is the 2m×2n complex matrix Ac=（（A<sub>1</sub>/A<sub>2</sub>）（-A<sub>2</sub>/A<sub>1</sub>））（see[1,2]）.We denote by A<sup>D</sup> the Drazin inverse of A∈H<sup>m×n</sup> which is the unique solution of the e-
基金This research is supported by the National Natural Science Foundation of China(No.11771076,11871145,12071070)the Qing Lan Project of Jiangsu Province,the Fundamental Research Funds for the Central Universities,the Postgraduate Research and Practice Innovation Program of Jiangsu Province(No.KYCX20_0074).
文摘Let A be a complex Banach algebra and J be the Jacobson radical of A.(1)We firstly show that a is generalized Drazin invertible in A if and only if a+J is generalized Drazin invertible in A/J.Then we prove that a is pseudo Drazin invertible in si if and only if a+J is Drazin invertible in A/J.As its application,the pseudo Drazin invertibility of elements in a Banach algebra is explored.(2)The pseudo Drazin order is introduced in A.We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order,then we prove that the pseudo Drazin order is a pre-order.
基金supported by the National Natural Science Foundation of China(Grant No.11901099)the Natural Science Foundation of Fujian Province(Grant No.2018J05004)。
文摘For a Banach algebra A with identity and a, b, c, d ∈ A, the relations between the extended g-Drazin inverse(resp. generalized strong Drazin inverse)of ac and that of bd are given, when bac = bdb and cac = cdb.
基金This work is supported by the National Natural Science Foundation of China(Nos.11801115,12071097,12042103)the Natural Science Foundation of the Heilongjiang Province(No.QC2018002)the Fundamental Research Funds for the Central Universities.
文摘In this paper,we give further results on the Drazin inverse of tensors via the Einstein product.We give a limit formula for the Drazin inverse of tensors.By using this formula,the representations for the Drazin inverse of several block tensor are obtained.Further,we give the Drazin inverse of the sum of two tensors based on the representation for the Drazin inverse of,a block tensor.
文摘For bounded linear operators A,B,C and D on a Banach space X,we show that if BAC=BDB and CDB=CAC then I-AC is generalized Drazin-Riesz invertible if and only if I-BD is generalized Drazin-Riesz invertible,which gives a positive answer to Question 4.9 in Yan,Zeng and Zhu[Complex Anal.Oper.Theory 14,Paper No.12(2020)].In particular,we show that Jacobson’s lemma holds for generalized Drazin-Riesz inverses.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12171083,11871145,12071070)the Qing Lan Project of Jiangsu Provincethe Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX22-0231)。
文摘Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.
文摘This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.
文摘Let A be a Banach algebra with unit e and a,b,c∈A,Mc=(a c 0 b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of is defined byσ_(gD)(α)={λ∈C:α-λe is not generalized Drazin invertible}.It is shown thatσ_(gD)(a)∪σ_(gD)(b)=σ_(gD)(M_(C))∪W_(2),where W_(g) is a union of certain holes σ_(gD) and W_(g)■σ_(gD)(a)∩σ_(gD)(b),or more finely.In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.
