Compact Operators on Hilbert Space
چکیده
Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most imitate the more familiar linear algebra of finite-dimensional operator theory. In addition, these are of considerable practical value and importance. We prove a spectral theorem for self-adjoint operators with minimal fuss. Thus, we do not invoke broader discussions of properties of spectra. We only need the CauchySchwarz-Bunyakowsky inequality and the definition of self-adjoint compact operator. It is true that various points here admit great generalization, and receive definitive treatment only in such general setting.