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Topological function-theoretic proofs in spectral theory

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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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References

  1. Douglas R., Pearcy C.,On the spectral theorem for normal operators, Proc. Camb. Phil. Soc.68 (1970), 393–400.

    Article  MATH  MathSciNet  Google Scholar 

  2. Douglas R.Banach Algebra Techniques in Operator Theory, Acad. Press, New York (1972).

    MATH  Google Scholar 

  3. Dunford N., Schwartz J.,Linear Operators, Spectral Theory, Vol II, Interscience Publ., New York, (1963).

    Google Scholar 

  4. Fell G. M., Kelley J. L.,An algebra of unbounded Operators, Proc. Nat. Acad. Sci USA (38) (1952), 592–598.

    Article  MATH  MathSciNet  Google Scholar 

  5. Kadison R. V., Ringrose J. R.,Fundamentals of the Theory of Operator algebras, Vol. I, Acad. Press, New York (1983).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Graduate School and University Center of The City University of New York, 10036, New York

    Fotios C. Paliogiannis

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  1. Fotios C. Paliogiannis
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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

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