MAPS PRESERVING SOME MULTIPLICATIVE STRUCTURES ON STANDARD JORDAN OPERATOR ALGEBRAS

Multiplicative bijective maps on standard operator algebras

multiplicative bijective maps on standard operator algebras

Jordan Maps on Standard Operator Algebras

Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing that on standard operator algebras over spaces with dimension at least 2, the bijective solutions of that second equation are automatically additive.

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

Close operator algebras and almost multiplicative maps

where A,B ⊂ B(H), and the distance between A⊗Mn and B ⊗Mn is measured in B(H) ⊗ Mn ∼= B(H). We also investigate the consequences of “complete closeness”, i.e. what can be said when dcb(A,B) is small? For example, if dcb(A,B) is small, then any projection p ∈ A ⊗ Mn can be suitably approximated by a projection q ∈ B ⊗ Mn, leading an isomorphism K0(A) → K0(B) which maps [p]0 to [q]0. This strateg...