Parfeny P. Saworotnow, "Diagonalization of a self-adjoint operator acting on a Hilbert module", International Journal of Mathematics and Mathematical Sciences, vol. 8, Article ID 167172, 7 pages, 1985. https://doi.org/10.1155/S0161171285000734
Diagonalization of a self-adjoint operator acting on a Hilbert module
For each bounded self-adjoint operator on a Hilbert module over an -algebra there exists a locally compact space and a certain -valued measure such that is isomorphic to and 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.
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