This talk discusses a conjecture of R. V. Kadison and myself. Our conjecture is that each one-to-one linear map of one unital C*-algebra onto another that preserves the identity is a Jordan isomorphism if it maps the invertible elements of the first C*-algebra onto the invertible elements of the other C*-algebra. Connections are shown between this conjecture and Cartan’s uniqueness theorem. 1. ...

A geometric method for the design of a minimal-order dynamic feedforward compensator cancelling the minimum-phase invariant zeros of a linear multivariable system, while preserving the properties of controllability, observability, and right invertibility is discussed. The method is illustrated for continuous-time, non-strictly proper systems. Nonetheless, it also applies to strictly-proper syst...

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...

1. Introduction. The investigation leading to this publication was motivated by a desire to try to understand the structure of a linear unital mapping ϕ from a unital algebra A of matrices contained in M h (C) into M n (C) which has the property that an invertible element in A is mapped into an invertible in M n (C). The interest in this question was raised by some earlier results on a linear i...