Applications of Wigner’s theorem to positive maps preserving norm of operator products

Abstract

We apply Wigner’s theorem to positive maps on standard operator algebras that preserve norm of operator products or sum of singular values of operator products. It follows that such preservers are of the form ϕ(A) = U AU* with U either a unitary or antiunitary operator.

Keywords

Wigner’s theorem / preserver problem / operator algebra / norm / singular value / 47B01

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