08a. Operators on Hilbert spaces
نویسنده
چکیده
Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most closely imitate finite-dimensional operator theory. In addition, compact operators are important in practice. We prove a spectral theorem for self-adjoint compact operators, which does not use broader discussions of properties of spectra, only using the Cauchy-Schwarz-Bunyakowsky inequality and the definition of selfadjoint compact operator.
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