Local automorphisms and derivations on ℬ(ℋ)

Let A {A} be an algebra. A mapping θ : A ⟶ A θ :{A} {A} is called a 2 2 -local automorphism if for every a , b ∈ A a,b∈ {A} there is an automorphism θ a , b : A ⟶ A θ a,b:{A} {A} , depending on a a and b b , such that θ a , b ( a ) = θ ( a ) θ a,b(a)=θ (a) and θ a , b ( b ) = θ ( b ) </m