Let A be a complex diagonalizable matrix with two distinct nonzero eigenvalues λ and μ, the Yang-Baxter-like matrix equation AXA = XAX is reconsidered. We correct and improve the results in Shen et al ...

We construct a pure state on the C*-algebra 𝓑(ℓ₂) of all bounded linear operators on ℓ₂, which is not diagonalizable [i.e., it is not of the form limu⩽T(ek), ek⩾ for any orthonormal basis (ek)kϵℕ of ...