Isomorphisms of 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.

Multiplicative bijective maps on standard operator algebras

Isomorphisms of Hilbert C*-Modules and ∗-Isomorphisms of Related Operator C*-Algebras

Let M be a Banach C*-module over a C*-algebra A carrying two A-valued inner products 〈., .〉1, 〈., .〉2 which induce equivalent to the given one norms on M. Then the appropriate unital C*-algebras of adjointable bounded A-linear operators on the Hilbert A-modules {M, 〈., .〉1} and {M, 〈., .〉2} are shown to be ∗-isomorphic if and only if there exists a bounded A-linear isomorphism S of these two Hi...

multiplicative bijective maps on standard operator algebras

Linear Orthogonality Preservers of Standard Operator Algebras

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...