Quasi-multiplier homotopes of ternary rings of operators

Abstract

We study associative products x*zy=xzy on a ternary ring of operators X, where z ∈ X* is contractive. Completely isometric isomorphisms are characterized by the orbit of the parameter under ternary isomorphisms. For every such parameter, we compute the Jacobson radical and show that it has cube zero. For closed-range parameters, the semisimple quotient is completely boundedly isomorphic to a C*-corner. For nonzero closed-range parameters on B(H,K), the existence of a bounded algebra isomorphism is equivalent to the existence of a completely bounded one. These isomorphism classes are determined by the dimensions of the range, kernel, and cokernel. We also obtain an explicit divided-difference functional calculus and extend the closed-range results to adjointable operators on Hilbert C*-modules.