Banach代数中的伪Drazin逆

Pub Date : 2021-06-01 DOI:10.4208/cmr.2021-0013

Jianlong Chen

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引用次数: 1

摘要

设A是一个复巴拿赫代数，J是A的雅各布森根。(1)首先证明a在a中广义Drazin可逆当且仅当a+ J在a /J中广义Drazin可逆。然后证明a在a中是伪Drazin可逆的当且仅当a+ J在a /J中是Drazin可逆的。作为应用，探讨了Banach代数中元素的伪Drazin可逆性。(2)在A中引入伪Drazin顺序。给出了A中元素具有伪Drazin阶的充分必要条件，并证明了伪Drazin阶是一个预阶。AMS学科分类:15A09, 16U90, 46H05

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The Pseudo Drazin inverses in Banach Algebras

Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if and only if a+ J is Drazin invertible in A /J. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in A . We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order. AMS subject classifications: 15A09, 16U90, 46H05

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