Abstract
Let \({\mathcal {B}}(X)\) be the algebra of all bounded linear operators on Banach space X. For \(T\in {\mathcal {B}}(X)\) and \(\lambda \in \mathbb {C}\), let \(X_{T}(\{ \lambda \})\) denotes the local spectral subspace of T associated with \(\{\lambda \}\). We determine the forms of mappings (not necessarily linear) \(\phi :{\mathcal {B}}(X)\rightarrow {{\mathcal {B}}(X)}\) that preserve the local spectral subspace of either sum, product of operators or triple product of operators associated with a singleton.
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Benbouziane, H., Ech-Chérif Elkettani, M. & Herrou, I. Local spectral subspace preservers. Rend. Circ. Mat. Palermo, II. Ser 68, 293–303 (2019). https://doi.org/10.1007/s12215-018-0359-5
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DOI: https://doi.org/10.1007/s12215-018-0359-5