Authors | Mohsen Niazi,, |
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Journal | Archiv der Mathematik |
Page number | 157-164 |
Serial number | 104 |
Volume number | 2 |
IF | 0.5 |
Paper Type | Full Paper |
Published At | 2015 |
Journal Grade | ISI |
Journal Type | Typographic |
Journal Country | Belgium |
Journal Index | JCR،Scopus |
Abstract
We prove that, for a complex Hilbert space H with dimension bigger or equal than three, every linear mapping T : B(H) → B(H) satisfying the 3-local property is a *-monomorphism, that is, every linear mapping T : B(H) → B(H) satisfying that for every a in B(H) and every ξ, η in H, there exists a *-automorphism π a,ξ,η : B(H) → B(H), depending on a, ξ, and η, such that T(a)(ξ) = π a,ξ,η (a)(ξ), and T(a)(η) = π a,ξ,η (a)(η), is a *-monomorphism. This solves a question posed by Molnár in (Arch Math 102:83–89 2014).
tags: bilocal *-automorphism, 3-local property, extreme-strong-local *-automorphism, *-monomorphism, unitary equivalence, bilocal unitary equivalence