International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1985 / Article

Open Access

Volume 8 |Article ID 167172 | https://doi.org/10.1155/S0161171285000734

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

Received18 Jan 1984

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 L2(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.

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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