Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes

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 Makagon and Salehi (1986) and Rosenberg (1982) 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 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.