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Additive mappings in algebras of unbounded operators preserving operators of rank one

W. Timmermann
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Abstract

Let $ \mathcal D$ be a dense linear manifold in a Hilbert space $\mathcal H$ and let $L^+(\mathcal D)$ be the *-algebra of all linear operators $A$ such that $A \mathcal D \subset \mathcal D, A^* \mathcal D \subset \mathcal D$. Denote by $F(\mathcal D)$ the *-ideal of $L^+(\mathcal D)$ consisting of all finite-rank operators. A characterization of the structure of additive mappings of $F(\mathcal D)$ preserving operators of rank one or projections of rank one is given. The corresponding results for algebras of bounded operators on Banach spaces were given by P. uSemrl.

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W. Timmermann. 2005-03-07. Additive mappings in algebras of unbounded operators preserving operators of rank one. https://arxiv.org/abs/math/0405545

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