A new theorem on the injectivity of the linear operators on separable Hilbert spaces is introduced, extending the Injectivity Criteria from [1]. The Corollary puts it together with the Injectivity Criteria backing up the discretization methods, Galerkin and the finite rank operators orthogonal projections.
Their matrix representations of the integral operator on the dense family of approximation subspaces, almost coincide and, in both cases we proved the injectivity of the integral operator used by Alcantara-Bode equivalent formulation of the Riemann Hypothesis.
Some observations regarding the sparsity of the matrix representations of the integral operators projections are made too.
subjclass: 65R99, 47G10, 45P05