论文标题
关于操作员的合同的Banach代数的评论
A Remark on Contractible Banach Algebras of Operators
论文作者
论文摘要
对于Banach代数$ a $，我们说如果$（a \ otimes 1）m = m（1 \ otimes a）$ in a $中的$（1 \ otimes a）$，则元素$ m $ in $ a \ otimes^γa$是超交换器。 Banach代数的对角线是一种超交换器，其对角线映射下的图像为$ 1 $。众所周知，如果FF具有对角线，则Banach代数是可缩度的。 The main aim of this note is to show that for any Banach subalgebra $A\subseteq\mathcal{L}(X)$ of bounded linear operators on infinite-dimensional Banach space $X$, which contains the ideal of finite-rank operators, the image of any hyper-commutator of $A$ under the canonical algebra-morphism $ \ MATHCAL {l}（x）\ otimes^γ\ Mathcal {l}（x）\ to \ Mathcal {l}（x \ otimes^γx）$，消失。
For a Banach algebra $A$, we say that an element $M$ in $A\otimes^γA$ is a hyper-commutator if $(a\otimes 1)M=M(1\otimes a)$ for every $a\in A$. A diagonal for a Banach algebra is a hyper-commutator which its image under diagonal mapping is $1$. It is well-known that a Banach algebra is contractible iff it has a diagonal. The main aim of this note is to show that for any Banach subalgebra $A\subseteq\mathcal{L}(X)$ of bounded linear operators on infinite-dimensional Banach space $X$, which contains the ideal of finite-rank operators, the image of any hyper-commutator of $A$ under the canonical algebra-morphism $\mathcal{L}(X)\otimes^γ\mathcal{L}(X)\to\mathcal{L}(X\otimes^γX)$, vanishes.
