adjoint space
1.Each observable is represented by a densely defined Hermitian (or self-adjoint) linear operator acting on the state space.
2.Bellman Inequality Tr((AB)2n )≤Tr(A2n B2n) on Hilbert space is proofed to be valid for operators belonging to the real self-adjoint trace class.
4.In this paper a sufficient condition for mixed finite element space of lowest order for Laplacian Equation is derived and a new interpolation operator is constructed. These results are applied to prove the optimal L∞-error estimates for the mixed finite element solution, the adjoint vector function and its divergence.
