Given unital Banach algebras $A$ and $B$ and elements $ain A$ and $bin B$,the Drazin spectrun of $aotimes bin Aoverline{otimes} B$ will be fullycharacterized, where $Aoverline{otimes} B$ is a Banach algebra that is thecompletion of $Aotimes B$ with respect to a uniform crossnorm. To this end,however, first the isolated points of the spectrum of $aotimes binAoverline{otimes} B$ need to be characterized. On the other hand, givenBanach spaces $X$ and $Y$ and Banach space operators $Sin L(X)$ and $TinL(Y)$, using similar arguments the Drazin spectrum of $au_{ST}in L(L(Y,X))$,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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