Given unital Banach algebras $A$ and $B$ and elements $a\in A$ and $b\in B$,the Drazin spectrun of $a\otimes b\in A\overline{\otimes} B$ will be fullycharacterized, where $A\overline{\otimes} B$ is a Banach algebra that is thecompletion of $A\otimes B$ with respect to a uniform crossnorm. To this end,however, first the isolated points of the spectrum of $a\otimes b\inA\overline{\otimes} B$ need to be characterized. On the other hand, givenBanach spaces $X$ and $Y$ and Banach space operators $S\in L(X)$ and $T\inL(Y)$, using similar arguments the Drazin spectrum of $\tau_{ST}\in L(L(Y,X))$,the elementary operator defined by $S$ and $T$, will be fully characterized.
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机译：给定单一的Banach代数$ A $和$ B $以及元素$ a \ in A $和$ b \ in B $，则$ a \ otimesb \ A \ overline {\ otimes} B $的Drazin谱将被完全表征，其中$ A \ overline {\ otimes} B $是Banach代数，是相对于统一交叉范数的$ A \ otimes B $的完成。但是，为此，首先需要确定$ a \ otimes b \ inA \ overline {\ otimes} B $频谱中的孤立点。另一方面，使用类似的参数，给定Banach空间$ X $和$ Y $以及Banach空间运算符$ S \ in L（X）$和$ T \ inL（Y）$，使用Drazin频谱$ \ tau_ {ST} \在L（L（Y，X））$中，由$ S $和$ T $定义的基本运算符将得到充分表征。
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