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arXiv · 2203.15715

Commuting maps with the Mean Transform under Jordan product

Fadil Chabbabi
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Abstract

In this article, we give a complete characterization of the bijective maps which commute with the mean transform under Jordan product. The main result is the following : Let $H,K$ be two complex Hilbert spaces and $Φ:B(H) \to B(K)$ be a bijective map, then $$ \mathcal {M}(Φ(A)\circΦ(B))=Φ(\mathcal{M}(A\circ B)) \;\; \text{for all}\;\; A, B \in B(H)$$ if and only if there exists a unitary or anti-unitary operator $U:H\to K $ such that, $$ Φ(T)= UTU^* \; \text{for all} \;T\in B(H).$$

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Fadil Chabbabi. 2022-03-29. Commuting maps with the Mean Transform under Jordan product. https://arxiv.org/abs/2203.15715

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