Nonlinear mappings preserving productXY+YX∗on factor von Neumann algebras

Nonlinear maps preserving Jordan triple η-⁎-products

“…Du [1] established that any bijective map between von Neumann algebras without central abelian projections preserving the Jordan (-1)- * -product is a sum of linear and conjugate linear * -isomorphisms. In [6], C.J. Li, F.Y.…”

Nonlinear mappings preserving Jordan multiple ∗– product on factor von Neumann algebras

“…[4][5][6][7] In [8], let A and B be two factor von Neumann algebras, the authors studied the nonlinear bijective map In this paper, we will expand the result of reference. [10] Let A and B be two factor von Neumann algebras. For A 1 , A 2 , · · · , A n ∈ A define by A 1 • A 2 • · · · • A n the Jordan multiple * −product of A 1 , A 2 , · · · , A n .…”

“…In particular, if the von Neumann algebras A and B are type I factors, then is a unitary isomorphism or a conjugate unitary isomorphism. Finally, we can known that reference [10] is our special example.…”

“…Lemma 1.3 [10] Let A be an arbitrary factor von Neumann algebra with identity operator I and A ∈ A. Then AB + B A * = 0 for all B ∈ A implies that A ∈ iRI (i is the imaginary number unit).…”

Non-linear ξ-Jordan *-derivations on von Neumann algebras

“…Recently, many authors pay more attention to the mappings preserving the ξ -Jordan *-product between *-algebra (see, e.g. [6][7][8]). …”