By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the ope...By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.展开更多
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's suf...This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.展开更多
文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和...文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和的算子矩阵.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banachmodules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadraticmapping in Banach modules over a unital...The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banachmodules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadraticmapping in Banach modules over a unital Banach algebra.展开更多
Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse f...Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a + b∈A^(qnil) under the condition that a,b∈A^(qnil),aba = 0 and ab^2= 0 and then the explicit expressions for the generalized Drazin inverse of the sum a + b under some newconditions are given. Also, some known results are extended.展开更多
We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra...We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.展开更多
在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin...在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin可逆的,当且仅当aa~(a+b)是伪Drazin可逆的,当且仅当aa~(a+b)bb~是伪Drazin可逆的.此时,(a+b)~=(aa~(a+b))~+sum from n=0 to ∞φ-(n(n+1))/2(1)(b~)^(n+1)(-a)~n(1-aa~).展开更多
基金This Work was supported by the National Natural Science Foundation of China(Grant No.10171014)the Natural Science Foundation of Fujian Province of China.
文摘By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
基金supported by the National Natural Science Foundation of China(Grant No.10471025)the Natural Science Foundation of Fujian Province of China(Grant Nos.F0210014&Z0511019).
文摘This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金Project supported by grant No.KRF-2000-015-DP0038.
文摘The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banachmodules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadraticmapping in Banach modules over a unital Banach algebra.
基金The National Natural Science Foundation of China(No.11371089,11371165)the Natural Science Foundation of Jilin Province(No.20160101264JC)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Fundamental Research Funds for the Central Universities,the Foundation of Graduate Innovation Program of Jiangsu Province(No.KYZZ15-0049)
文摘Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a + b in terms of a,b,a^d,b^d is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a + b∈A^(qnil) under the condition that a,b∈A^(qnil),aba = 0 and ab^2= 0 and then the explicit expressions for the generalized Drazin inverse of the sum a + b under some newconditions are given. Also, some known results are extended.
基金supported by the Engineering and Physical Sciences Research Council,UK(Grant No.EP/R044228/1).
文摘We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.
文摘在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin可逆的,当且仅当aa~(a+b)是伪Drazin可逆的,当且仅当aa~(a+b)bb~是伪Drazin可逆的.此时,(a+b)~=(aa~(a+b))~+sum from n=0 to ∞φ-(n(n+1))/2(1)(b~)^(n+1)(-a)~n(1-aa~).
