论文标题
巢代数的三元衍生物
Ternary derivations of nest algebras
论文作者
论文摘要
假设$ x $是一个（真实或复杂的）Banach空间，$ DIMX \ geq 2 $，而$ \ Mathcal {n} $是$ x $上的嵌套，每当$ x $ in $ x $中的每个$ n $ in $ x $ in $ x $均以$ x $补充。 $ alg \ Mathcal {n} $的三元推导是$ alg \ alg \ Mathcal {n} $的线性三重映射$（γ，δ，τ）$，因此$ a，b +a for Alg a，b \ a b \ a b \ a b \ b \ ing in alg a alg \ nath} $我们表明，对于线性地图$δ$，$ alg \ Mathcal {n} $上的$τ$，存在一个唯一的线性地图$γ$来自$ alg \ alg \ Mathcal {n} $ to $ alg \ alg \ Mathcal {n} $ $ ung $γ（a）= ra $ r $ r $， $（γ，δ，τ）$是$ alg \ Mathcal {n} $的三元推导，并且仅当$δ$，$τ$，$δ$δ（a）$δ（a）b+aτ（a）b+aτ（b）= 0 $ for任何$ a $ a $，$ a $，$ b $ in $ alg ing in $ alg ing in $ alg \ alg alg \ nathcal \ nathcal \ nathcal {n} $ with $ ab = 0 $ ab = 0 $ ab = 0 $ = 0 $ = 0 $。我们还证明，$ alg \ Mathcal {n} $上的每个三元派生都是内部三元派生。我们的结果适用于（右或左）中心化的（通过零产品，局部右（左）中央位置，右（左）理想保留地图和嵌套代数上的局部推导。
Suppose that $X$ is a (real or complex) Banach space, $dimX \geq 2$, and $\mathcal{N}$ is a nest on $X$, with each $N$ in $\mathcal{N}$ is complemented in $X$ whenever $N_{-}=N$. A ternary derivation of $Alg\mathcal{N}$ is a triple of linear maps $(γ, δ, τ)$ of $Alg\mathcal{N}$ such that $γ(AB)=δ(A)B +Aτ(B)$ for all $A,B \in Alg\mathcal{N}$. We show that for linear maps $δ$, $τ$ on $Alg\mathcal{N}$ there exists a unique linear map $γ$ from $Alg\mathcal{N}$ into $Alg\mathcal{N}$ defined by $γ(A)=RA+AT$ for some $R$, $T$ in $Alg\mathcal{N}$ such that $(γ, δ, τ)$ is a ternary derivation of $Alg\mathcal{N}$ if and only if $δ$, $τ$ satisfy $δ(A)B+Aτ(B)=0$ for any $A$,$B$ in $Alg\mathcal{N}$ with $AB=0$. We also prove that every ternary derivation on $Alg\mathcal{N}$ is an inner ternary derivation. Our results are applied to characterize the (right or left) centralizers and derivations through zero products, local right (left) centralizers, right (left) ideal preserving maps and local derivations on nest algebras.
