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Mappings preserving zero products

M. A. Chebotar, W.-F. Ke, P.-H. Lee, N.-C. Wong (2003)

Studia Mathematica

Let θ : ℳ → 𝓝 be a zero-product preserving linear map between algebras. We show that under some mild conditions θ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C*-algebras and W*-algebras.

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