In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

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.

Let X be an infinite-dimensional separable real or complex Banach space and A a closed standard operator algebra on X. Then every local automorphism of A is an automorphism. The assumptions of infinitedimensionality, separability, and closeness are all indispensable.

Abstract Let χ be a Banach space of dimension n > 1 and

We study a class of matrix function algebras, here denoted T (Cn). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T (Cn). We use point derivations and information about n×n matrices to show that every T (Cn)-valued derivation on T (Cn) is inner. Certain matrix function algebras arise in some standard constructions...