Abstract
In this paper, the spectral theorem and related characterizations of the spectrum and the spectral projections for bounded self adjoint and normal operators on a Hilbert space, are proved in purely topological —function theoretic terms. The basis for such a development, is the Gelfand—Naimark theorem for commutativeC *-algebras and the fact that the structure space of the (abelian) von Neumann algebra generated by the operator is a Stonean space.
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Paliogiannis, F.C. Topological function-theoretic proofs in spectral theory. Rend. Circ. Mat. Palermo 44, 21–44 (1995). https://doi.org/10.1007/BF02849804
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DOI: https://doi.org/10.1007/BF02849804