Publications Repository - Gdańsk University of Technology

We prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained for stochastic one-parameter contiuous semigroups.

Authors

• prof. dr hab. inż. Wojciech Bartoszek link open in new tab ,
• Krzysztof Bartoszek