Linear operators in Hilbert space
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The purpose of this paper is to present a modified version of Riesz's proof of the spectral theorem for bounded linear operators. The modifications employed are those suggested by S. K. Berberian (5, page 1049). The basic properties of Hilbert space are presented in Chapter I. Chapter II is a discussion of linear operators which includes consideration of functionals, self-adjoint operators, and the spectrum of an operator. The spectral decomposition of a bounded self-adjoint operator is presented in Chapter III. The material in the paper is based primarily on the references in the bibliography. Most of the nontrival proofs have been carried out in detail.
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