Additive preservers on Banach algebras
Copyright policy )Additive preservers on Banach algebras
Summary: It is shown that an additive, surjective mapping \(\Phi:\text{soc}({\mathcal A})\to\text{soc}({\mathcal A})\), preserving rank-one idempotents and their linear spans in both directions, is a real-linear Jordan isomorphism provided that \(\mathcal A\) is a semiprime Banach algebra with no nonzero central elements in its socle.
Linear operators on Banach algebras, additive preserver, socle, rank, Ideals and subalgebras, semiprime Banach algebra, Linear transformations, semilinear transformations, minimal idempotent, Representations of topological algebras
Linear operators on Banach algebras, additive preserver, socle, rank, Ideals and subalgebras, semiprime Banach algebra, Linear transformations, semilinear transformations, minimal idempotent, Representations of topological algebras
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