Abstract
Let \(\mathcal {A}\) be a unital Banach algebra and \(\mathcal {M}\) be a unital Banach \(\mathcal {A}\)-bimodule. The main results characterize a continuous linear map \(\varphi :\mathcal {A}\rightarrow \mathcal {M}\) that satisfies \(a\varphi (a^{-1})=\varphi (1)\) or \(a\varphi (a^{-1})+ \varphi (a^{-1}) a=2\varphi (1)\) for all \(a\) in principal component of invertible elements of \(\mathcal {A}\). The proof is based on the consideration of a continuous bilinear map satisfying a related condition.
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Communicated by Mohammad Sal Moslehian.
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Ghahramani, H. On Centralizers of Banach Algebras. Bull. Malays. Math. Sci. Soc. 38, 155–164 (2015). https://doi.org/10.1007/s40840-014-0011-2
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DOI: https://doi.org/10.1007/s40840-014-0011-2