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Let ℳ, 𝒩 be von Neumann algebras with no central summands of type I1 or I2. If Φ : ℳ → 𝒩 is a multiplicative *-Lie isomorphism, then there is a central projection E ∈ 𝒩 such that modulo a centre-valued map which annihilates commutators, EΦ is a linear Lie *-homomorphism and (I − E)Φ is a conjugate linear Lie *-homomorphism. [ABSTRACT FROM PUBLISHER]

In this article, we get a complete classification of distance preserving surjective maps Φ between nest algebras acting on separable Hilbert spaces. [ABSTRACT FROM AUTHOR]

Let H be an infinite-dimensional complex separable Hilbert space and  [image omitted] denote the algebra of all bounded linear operators acting on H. We show that an additive continuous surjective map Φ on  [image omitted] is asymptotic similarity preserving if and only if it is similarity preserving, and in turn, if and only if there exist a scalar c and an invertible bounded linear or conjugate linear operator A on H such that either Φ(T)=cATA-1 for all T or Φ (T)=cAT*A-1 for all T. [ABSTRACT FROM AUTHOR]