THE USE OF 2F/(I+F^*F) TO PROOF THE SPECTRAL THEOREM FOR UNBOUNDED SELF-ADJOINT OPERATORS

Abstract

A number of proofs of the spectral theorem for unbounded self-adjoint operators in a complex Hilbert space have been developed. Most of them uses a bounded transform to get the desired results. In this paper, we proof the same theorem using a new a bounded self-adjoint operator transform constructed due to the mapping z↦2z1+z2-1  for a complex number z .

Keywords: Unbounded operators, Self-adjoint operators, Spectral theorem.