International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 669-675
doi:10.1155/S0161171285000734
Diagonalization of a self-adjoint operator acting on a Hilbert module
Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA
Received 18 January 1984
Copyright © 1985 Parfeny P. Saworotnow. 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.
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.