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Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes. (English) Zbl 0681.60037
Let B be a Banach space and H and K two Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of A. Makagon and H. Salehi [see Stud. Math. 85, 257-297 (1987; Zbl 0625.60042)] and M. Rosenberg [see Pac. J. Math. 103, 135-161 (1982; Zbl 0509.46039)] on the dilation of L(K,H)- valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures.
These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as an application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.
Reviewer: A.G.Miamee
60G10 Stationary stochastic processes
60B05 Probability measures on topological spaces
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