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正交投影和幂等算子线性组合的w-加权drazin逆  [PDF]
内蒙古大学学报(自然科学版) , 2015, DOI: 10.13484/j.nmgdxxbzk.20150404
Abstract: 借助空间分解,得到了在满足条件pqp=p时,无穷维hilbert空间中的正交投影算子p和幂等算子q的线性组合mp+nq的w-加权drazin可逆性及其w-加权drazin逆的表达式.
(u,v)-idempotent matrices and essential (m,l)-idempotent matrices

福州大学学报(自然科学版) , 2015, DOI: 10.7631/issn.1000-2243.2015.03.0311
Abstract: 证明了(u,v)幂等矩阵与本质(m,l)幂等矩阵的互相确定关系,由此给出了求(u,v)幂等矩阵的Jordan标准形的方法,这种方法不依赖通常的求Jordan标准形的算法,只涉及到矩阵方幂的秩和u-v次单位根εi所确定的矩阵秩最后得到以矩阵秩为基本工具的,判定(u1,v1)幂等矩阵与(u2,v2)幂等矩阵相似的充分必要条件.
It has been proved that (u,v)-idempotent matrices and essential (m,l)-idempotent matrices can be determined by each other. Then it gives us a method to work out the Jordan canonical form of a (u,v)-idempotent matrix,independently on the usual method of the Jordan canonical form,only referring to the ranks of matrix powers and u-v-th unity roots εi . By using ranks of matrices as a basic tool,it also obtains some sufficient and necessary conditions for a (u1,v1)-idempotent matrix to be similar to a (u2,v2)-idempotent one

- , 2015,
Abstract: 本文研究了幂等扩张的有界分配格的同余可换性问题.利用幂等扩张的有界分配格的对偶理论,得到了同余可换的幂等扩张的有界分配格的一个充分必要条件,推广了Davey和Priestley关于有界分配格的一些结果.
In this paper, we study the idempotent extended bounded distributive lattices whose congruence are permutable. By the dual theory of idempotent extended distributive lattices, we get a necessary and sufficient condition of congruence permutable idempotent extended distributive lattices. Some results obtained by Davey and Priestley on bounded distributive lattices are generalized
Invertibility of the combination of two idempotent matrices which products is idempotent matrix

曹元元,左可正,熊 瑶
CAO Yuanyuan
,ZUO Kezheng,XIONG Yao

- , 2017,
Abstract: 利用幂等矩阵的性质及两个幂等矩阵的和与差的可逆性,研究了两个幂等矩阵P,Q在条件(PQ)2=PQ下,它们的组合T=aP+bQ+cPQ+dQP+ePQP+fQPQ+g(QP)2,(a,b,c,d,e,f,g∈?,ab≠0)的可逆性,并给出它的求逆公式.
The Expression of the Generalized Drazin Inverse of
Xiaoji Liu,Dengping Tu,Yaoming Yu
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/412872
Abstract: We investigate the generalized Drazin inverse of ? over Banach spaces stemmed from the Drazin inverse of a modified matrix and present its expressions under some conditions.
The Drazin spectrum in Banach algebras  [PDF]
Enrico Boasso
Mathematics , 2013,
Abstract: Several basic properties of the Drazin spectrum in Banach algebras will be studied. As an application, some results on meromorphic Banach space operators will be obtained.
关于两个幂等矩阵组合群逆的探讨 Discussions on the Group Inverses of Combinations of Two Idempotent Matrices  [PDF]
- , 2018,
Abstract: 运用矩阵零空间的性质证明了复数域上两个不同的非零幂等矩阵P,Q的组合a_1P+b_1Q+a_2PQ+b_2QP+…+a_(2n-1)(PQ)~(n-1 )P+b_(2n-1)(QP)~(n-1 )Q+a_(2n)(PQ)~n(其中a_1,b_1,…,b_(2n-1),a_(2n)∈C,a_1,b_1≠0)在条件(QP)~n=0(n≥2)下的秩与系数的选取无关,进而证明了其群逆存在.另外,还得到了组合aP+bQ+cPQ+dQP在条件(QP)~n=0下的群逆表达式
Additive Property of Drazin Invertibility of Elements  [PDF]
Long Wang,Huihui Zhu,Xia Zhu,Jianlong Chen
Mathematics , 2013,
Abstract: In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = \lambda ba$, we show that $a-b$ is Drazin invertible if and only if $aa^{D}(a-b)bb^{D}$ is Drazin invertible. Next, we give explicit representations of $(a+b)^{D}$, as a function of $a, b, a^{D}$ and $b^{D}$, under the conditions $a^{3}b = ba$ and $b^{3}a = ab$.
Idempotent mathematics and interval analysis  [PDF]
Grigori Litvinov,Viktor Maslov,Andrei Sobolevskii
Mathematics , 1999,
Abstract: A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.
Maps Completely Preserving Involutions and Maps Completely Preserving Drazin Inverse  [PDF]
Hongmei Yao,Baodong Zheng,Gang Hong
ISRN Applied Mathematics , 2012, DOI: 10.5402/2012/251389
Abstract: Let and be infinite dimensional Banach spaces over the real or complex field , and let and be standard operator algebras on and , respectively. In this paper, the structures of surjective maps from onto that completely preserve involutions in both directions and that completely preserve Drazin inverse in both direction are determined, respectively. From the structures of these maps, it is shown that involutions and Drazin inverse are invariants of isomorphism in complete preserver problems. 1. Introduction In the last decades, the study of preserver problems is an active topic in operator algebra or operator space theory (see [1]). In [2], the form of involutivity-preserving maps was given by using the known results of idempotence-preserving maps, and in [3], the authors gave the characterization of additive maps preserving Drazin inverse. These results showed that involutions and Drazin inverse are invariants of isomorphism in preserver problems. Since completely positive linear maps and completely bounded linear maps are very important in operator algebra or operator space theory [4], and the concept of completely rank nonincreasing linear maps was introduced by Hadwin and Larson in [5], many mathematicians began to focus on complete preserver problems, that is, characterizations of maps on operator spaces (subsets) that preserve some property (or invariant) completely [6]. Cui and Hou discussed the completely trace-rank-preserving linear maps and the completely invertibility-preserving linear maps in [7, 8], respectively. Subsequently, in [6, 9], general surjective maps between standard operator algebras that completely preserve invertibility or spectrum and that completely preserve spectral functions are studied, respectively, where a standard operator algebra is a norm closed subalgebra of some over a Banach space containing the identity and all finite-rank operators. Recently, in [10], the authors discussed completely idempotents preserving surjective maps and completely square-zero operators preserving surjective maps. These results showed that idempotents and square-zero operators are invariants of isomorphism in complete preserver problems. Since involutions and Drazin inverse are closely related to idempotents, it is interesting to consider whether the involutions and Drazin inverse are still invariants of isomorphism in complete preserver problems. Let and be Banach spaces over the real or complex field , and let be the Banach algebra of all bounded linear operators from to . An operator is called an involution (idempotent) if ( ), denoted by
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