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arXiv · 2203.16702

Weighted homomorphisms between C*-algebras

Eusebio Gardella·Hannes Thiel
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Abstract

We show that a bounded, linear map between C*-algebras is a weighted $\ast$-homomorphism (the central compression of a $\ast$-homomorphism) if and only if it preserves zero-products, range-orthogonality, and domain-orthogonality. It follows that a self-adjoint, bounded, linear map is a weighted $\ast$-homomorphism if and only if it preserves zero-products. As an application we show that a linear map between C*-algebras is completely positive, order zero in the sense of Winter-Zacharias if and only if it is positive and preserves zero-products.

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Eusebio Gardella, Hannes Thiel. 2022-03-30. Weighted homomorphisms between C*-algebras. https://arxiv.org/abs/2203.16702

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