Multilinear maps on products of operator algebras

On topological transitive maps on operator algebras

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Multiplicative bijective maps on standard operator algebras

on topological transitive maps on operator algebras

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

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.