Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜...Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜｜m A Banach algebra T is said to be Lie n-weakly amenable if all Lie derivations from T into its nth dual space T^（n） are standard. In this paper we investigate Lie n-weak amenability of a triangular Banach algebra T in relation to that of the algebras A, B and their action on the module M.展开更多
设A是有单位元的Banach代数,给定a,b∈A,记2×2上三角矩阵Mc=(a c 0 b)∈M2(A),其中c∈A.证明了στ(a)∪στ(b)=στ(Mc)∪W,其中当στ=σ时,Wσ(a)∩σ(b)是σ(Mc)的某些洞的并;当στ=σl时,Wσr(a)∩(σl(b)\σl(a))包含...设A是有单位元的Banach代数,给定a,b∈A,记2×2上三角矩阵Mc=(a c 0 b)∈M2(A),其中c∈A.证明了στ(a)∪στ(b)=στ(Mc)∪W,其中当στ=σ时,Wσ(a)∩σ(b)是σ(Mc)的某些洞的并;当στ=σl时,Wσr(a)∩(σl(b)\σl(a))包含在σl(a)的某些洞的并中,也包含在σl(Mc)的某些洞的并中;当στ=σr时,Wσl(b)∩(σr(a)\σr(b))包含在σr(b)的某些洞的并中,也包含在σr(Mc)的某些洞的并中.展开更多
设A是含单位元e的Banach代数,a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).本文提出了 Banach代数中元素的左、右广义Drazin可逆的概念.定义集合σgD(a)={λ∈C:a - λe不是广义Drazin可逆的}为元素a的广义Drazin谱.证明了σgD(a)∪σgD(a)=σg...设A是含单位元e的Banach代数,a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).本文提出了 Banach代数中元素的左、右广义Drazin可逆的概念.定义集合σgD(a)={λ∈C:a - λe不是广义Drazin可逆的}为元素a的广义Drazin谱.证明了σgD(a)∪σgD(a)=σgD(M_(c))∪W_(g),其中 W_(g) 是σgD (M_(c))的某些洞且W_(g)■σgD(a)∩σgD(b),或者更精细地W_(g)■σrgD(a)∩σlgD(b).此外,还研究了 Banach代数中元素的广义Drazin谱的其他性质.展开更多
文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A...文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A)^(■) 当且仅当b∈A^(■).最后,给出相应的数值例子来论证得到的结果.展开更多
Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B）...Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B） = 0 whenever AB = 0） if and only if it is a centralizer. Let 5 ： U →U be an additive map. It is also shown that the following four conditions are equivalent： （1） 5 is specially generalized derivable at zero point, i.e., 5（AB） = δ（A）B ＋ AS（B） - Aδ（I）B whenever AB = 0; （2） 5 is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ（AB） = δ（A）B ＋ Aτ1（B） = τ2（A）B ＋ Aδ（B） whenever AB = 0; （3） δ is a special generalized derivation; （4） δ is a generalized derivation. These results are then applied to nest algebras of Banach space展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117124411601010)
文摘Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜｜m A Banach algebra T is said to be Lie n-weakly amenable if all Lie derivations from T into its nth dual space T^（n） are standard. In this paper we investigate Lie n-weak amenability of a triangular Banach algebra T in relation to that of the algebras A, B and their action on the module M.
文摘设A是有单位元的Banach代数,给定a,b∈A,记2×2上三角矩阵Mc=(a c 0 b)∈M2(A),其中c∈A.证明了στ(a)∪στ(b)=στ(Mc)∪W,其中当στ=σ时,Wσ(a)∩σ(b)是σ(Mc)的某些洞的并;当στ=σl时,Wσr(a)∩(σl(b)\σl(a))包含在σl(a)的某些洞的并中,也包含在σl(Mc)的某些洞的并中;当στ=σr时,Wσl(b)∩(σr(a)\σr(b))包含在σr(b)的某些洞的并中,也包含在σr(Mc)的某些洞的并中.
文摘文章主要研究Banach代数上两个元素和的伪Drazin逆的存在性.通过Pierce分解,得到两个元素和具有伪Drazin逆的一些条件.然后,研究了Banach代数上反三角算子矩阵的伪Drazin逆的存在性,证明了反三角算子矩阵(1 b 10)∈M_(2)(A)^(■),b∈(A)^(■) 当且仅当b∈A^(■).最后,给出相应的数值例子来论证得到的结果.
基金supported by National Natural Science Foundation of China (Grant No. 11101250)supported by National Natural Science Foundation of China (Grant No. 11171249)Youth Foundation of Shanxi Province (Grant No. 2012021004)
文摘Let U = Tri（fit, M, B） be a triangular ring, where A and B are unital rings, and M is a faithful （A, B）-bimodule. It is shown that an additive map φ on U is centralized at zero point （i.e., ,φ（A）B = A,φ（B） = 0 whenever AB = 0） if and only if it is a centralizer. Let 5 ： U →U be an additive map. It is also shown that the following four conditions are equivalent： （1） 5 is specially generalized derivable at zero point, i.e., 5（AB） = δ（A）B ＋ AS（B） - Aδ（I）B whenever AB = 0; （2） 5 is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ（AB） = δ（A）B ＋ Aτ1（B） = τ2（A）B ＋ Aδ（B） whenever AB = 0; （3） δ is a special generalized derivation; （4） δ is a generalized derivation. These results are then applied to nest algebras of Banach space
