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2-LOCAL ISOMETRIES OF SOME NEST ALGEBRAS
Published online by Cambridge University Press: 18 December 2023
Abstract
Let H be a complex separable Hilbert space with $\dim H \geq 2$. Let $\mathcal {N}$ be a nest on H such that $E_+ \neq E$ for any $E \neq H, E \in \mathcal {N}$. We prove that every 2-local isometry of $\operatorname {Alg}\mathcal {N}$ is a surjective linear isometry.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
This research was partly supported by the National Natural Science Foundation of China (Grant No. 11871021.