Piecewise ⁎-homomorphisms and Jordan maps on C⁎-algebras and factor von Neumann algebras

Functional identities and their applications

“…This was shown in [14] and is also surveyed in [53,Section 7.2]. It is interesting to note that these algebraic results were later used for solving some seemingly unrelated preserver problems from functional analysis [36,80,111].…”

Functional identities and zero Lie product determined Banach algebras

“…For details, we refer to the survey paper [25] (in particular, see the discussion around [25,Theorem 2.2] which is one of the crucial results that inspired the study of the zpd and zLpd properties). It is also noteworthy that the interest in commutativity preservers on operator algebras has recently reemerged [12,20], and, as the author learned from a private communication with J. Hamhalter, the characterization of bijective linear maps between von Neumann algebras that preserve commutativity in both directions from [10] should be useful in these new studies. In the context of zLpd Banach algebras satisfying certain natural constraints (which have a clear description in von Neumann algebras), we will consider maps that preserve commutativity in one direction only.…”