ABSTRACT
Let p and q be idempotent elements in a complex unital algebra and let , . In the present note we will prove that is equivalent to p+q (resp. p−q) if (resp. ). In particular, is invertible if and only if p+q (resp. p−q) is invertible, where (resp. ). We will also give alternative proofs of some already existing results.
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Disclosure statement
No potential conflict of interest was reported by the authors.