Far Eastern Mathematical Journal

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Maps on the Algebras of Measurable Operators Preserving Zero and Jordan Zero-products

I. M. Juraev

2012, issue 2, P. 195–200

Abstract

In this paper, we prove that a continuous linear surjection from an algebra of measurable operators onto another one preserves zero products (resp. zero Jordan products) if and only if it is a non-zero scalar multiple of a homomorphism (resp. of an Jordan homomorphism).

Keywords: von Neumann algebras, measurable operator, topology of convergence in measure, trace, homomorphism, Jordan homomorphism

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References

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