Workshop in Analysis and Probability Seminar

Date: July 24, 2015

Time: 3:00PM - 4:00PM

Location: Blocker 220

Speaker: Rui Liu, Texas A&M University

Title: Dilations of Operator‐Valued Measures and Frames for Banach Spaces

Abstract: This talk is on a general dilation theory of operator-valued measures and frames for Banach spaces, motivated by the observation that there is a connection between the analysis of dual pairs of frames (both the discrete and the continuous theory) and the dilation theory of operator-valued measures on Banach spaces. As a continuation of a recent work (AMS memoir), we show that every operator-valued system of imprimitivity has dilation to a spectral system of imprimitivity acting on a larger Banach space, and we also prove that every operator-valued measure with bounded p-variation can be dilated to a projection-valued measure with the same variation property on a larger Banach space. This is undergoing joint work with David Larson, Deguang Han, and Bei Liu.