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Diagonalization of a self-adjoint operator acting on a Hilbert module

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  • Parfeny P. Saworotnow

Abstract

For each bounded self-adjoint operator T on a Hilbert module H over an H * -algebra A there exists a locally compact space m and a certain A -valued measure μ such that H is isomorphic to L 2 ( μ ) ⊗ A and T corresponds to a multiplication with a continuous function. There is a similar result for a commuting family of normal operators. A consequence for this result is a representation theorem for generalized stationary processes.

Suggested Citation

  • Parfeny P. Saworotnow, 1985. "Diagonalization of a self-adjoint operator acting on a Hilbert module," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:167172
    DOI: 10.1155/S0161171285000734
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