Comment on Maps preserving the dimension of fixed points of products of operators

2024/12/01 by Elouazzani, S., Elhodaibi, M., Saber, S.
#46J10 #47B48 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2412.01006

Abstract

Let B (X) be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space X. In this note, we show that a lemma used in the proof of the main result of [ Taghavi and Hosseinzadeh, linear and Multilinear algebra (2013) 1285-1292.] has an incorrect proof. Then, instead of such a lemma, we provide two elementary lemmas to obtain a proof of Taghavi and Hosseinzadeh's main result free of errors.

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• Maps preserving the fixed points of products of operators
• Fixed product preserving mappings on Banach algebras
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