Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only i...Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.展开更多
Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b unde...Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.展开更多
In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new...In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.展开更多
基金The NSF(11371233)of Chinathe Fundamental Research Funds(GK201301007)for the Central Universities
文摘Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.
基金The authors are highly grateful to the referees for their valuable comments and suggestions which greatly improved this paper.This research is supported by the National Natural Science Foundation of China(No.11801124)China Postdoctoral Science Foundation(No.2020M671068).
文摘Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.
基金The work was supported by the Research Fund Project of Guangxi University for Nationalities(No.2019KJQD03)Guangxi Natural Science Foundation(No.2018GXNSFDA281023)+2 种基金the National Natural Science Foundation of China(No.12061015)the Special Fund for Bagui Scholars of Guangxi(No.2016A17)the Education Innovation Program for 2019 Graduate Students(No.gxun-chxzs 2019026).
文摘In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.
