On some functional equations on standard operator algebras

On Some Functional Equations on Standard Operator Algebras

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) ⊆ L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T (A2n+1) = 2n+1 ∑ i=1 (−1)i+1Ai−1T (A)A2n+1−i, for all A ∈ A(X) and some fixed integer n ≥ 1. In this case T ...

Multiplicative bijective maps on standard operator algebras

multiplicative bijective maps on standard operator algebras

On Isomorphisms of Standard Operator Algebras

The aim of this paper is to show that between standard operator algebras every bijective map with a certain multiplicativity property related to the Jordan triple isomorphisms of associative rings is automatically additive.

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.