A densely-defined, closed, symmetric operator T has this quality if both T minus i and T plus i are surjective.
A densely-defined, closed, symmetric operator T has this quality if both T minus i and T plus i are surjective. If an operator is symmetric everywhere defined in a Hilbert space, then by a result of Hellinger and Toeplitz it is bounded and therefore must have this property. By the finite-dimensional spectral theorem, there is an orthonormal basis of a product space consisting of eigenvectors of this type of matrix. For a matrix of this kind, if and only if it is symmetric, the entries on the main diagonal must be real. For 10 points, give this term that describes an operator that is its own adjoint, or a matrix that is its own conjugate transpose.
A densely-defined, closed, symmetric operator T has this quality if both T minus i and T plus i are surjective.
Hermitian [accept self-adjoint before "adjoint"]