In this paper, we discuss several additional properties a power linear Keller map may have. The Structural Conjecture by Drużkowski in [Dru] asserts that two such properties are equivalent, but we show that one of this properties is stronger than the other. We even show that the property of linear triangularizability is strictly in between. Furthermore, we give some positive results for small d...

Let τ be a linear map from a unital C∗-algebra A to a von Neumann algebra B and let C be a unital C∗-algebra. A map T from a Hilbert A-module E to a von Neumann C-B module F is called a τ -map if 〈T (x), T (y)〉 = τ(〈x, y〉) for all x, y ∈ E. A Stinespring type theorem for τ -maps and its covariant version are obtained when τ is completely positive. We show that there is a bijective correspondenc...

For a positive integer n, let Mn be the set of n × n complex matrices. Suppose ‖ · ‖ is the Ky Fan k-norm with 1 ≤ k ≤ mn or the Schatten p-norm with 1 ≤ p ≤ ∞ (p 6= 2) on Mmn, where m,n ≥ 2 are positive integers. It is shown that a linear map φ : Mmn →Mmn satisfying ‖A⊗B‖ = ‖φ(A⊗B)‖ for all A ∈Mm and B ∈Mn if and only if there are unitary U, V ∈ Mmn such that φ has the form A ⊗ B 7→ U(φ1(A) ⊗ ...