Local automorphisms and derivations on ℬ (ℋ)
P Šemrl�- Proceedings of the American Mathematical Society, 1997 - ams.org
P Šemrl
Proceedings of the American Mathematical Society, 1997•ams.orgLet ${\mathcal {A}} $ be an algebra. A mapping $\theta:{\mathcal {A}}\longrightarrow
{\mathcal {A}} $ is called a $2 $-local automorphism if for every $ a, b\in {\mathcal {A}} $
there is an automorphism $\theta _ {a, b}:{\mathcal {A}}\longrightarrow {\mathcal {A}} $,
depending on $ a $ and $ b $, such that $\theta _ {a, b}(a)=\theta (a) $ and $\theta _ {a,
b}(b)=\theta (b) $(no linearity, surjectivity or continuity of $\theta $ is assumed). Let $ H $ be
an infinite-dimensional separable Hilbert space, and let ${\mathcal {B}}(H) $ be the algebra�…
{\mathcal {A}} $ is called a $2 $-local automorphism if for every $ a, b\in {\mathcal {A}} $
there is an automorphism $\theta _ {a, b}:{\mathcal {A}}\longrightarrow {\mathcal {A}} $,
depending on $ a $ and $ b $, such that $\theta _ {a, b}(a)=\theta (a) $ and $\theta _ {a,
b}(b)=\theta (b) $(no linearity, surjectivity or continuity of $\theta $ is assumed). Let $ H $ be
an infinite-dimensional separable Hilbert space, and let ${\mathcal {B}}(H) $ be the algebra�…
Abstract
Let be an algebra. A mapping is called a -local automorphism if for every there is an automorphism , depending on and , such that and (no linearity, surjectivity or continuity of is assumed). Let be an infinite-dimensional separable Hilbert space, and let be the algebra of all linear bounded operators on . Then every -local automorphism is an automorphism. An analogous result is obtained for derivations. References
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