Korovkin-type results and doubly stochastic transformations over Euclidean Jordan algebras

A well-known theorem of Korovkin asserts that if $$\{T_k\}$$ is a sequence positive linear transformations on C[a, b] such $$T_k(h)\rightarrow h$$ (in the sup-norm b]) for all $$h\in \{1,\phi ,\phi ^2\}$$ , where $$\phi (t)=t$$ [a, b], then C[a,b]$$ . In particular, T transformation $$T(h)=h$$ identity transformation. this paper, we present some analogs these results over Euclidean Jordan algebras. We show algebra $${{\mathcal {V}}}$$ \{e,p,p^2\}$$ e unit element in and p an with distinct eigenvalues, $$T=T^*=I$$ (the transformation) span frame corresponding to spectral decomposition p; consequently, coincides (more generally, automorphism ) frame, it doubly stochastic. also sequential weak-majorization versions.