Events for 07/24/2015 from all calendars

Workshop in Analysis and Probability Seminar

Time: 11:00AM - 12:00PM

Location: Blocker 220

Speaker: Ryan Causey, University of South Carolina

Title: A Dichotomy for Tress and Applications

Abstract: We discuss the use of trees and ordinal indices in Banach space theory. We present a few related dichotomies for trees and discuss a number of applications. Applications include measuring the Bourgain l_p or c₀ indices and Szlenk indices of Banach spaces and operators, deducing generalizations of James' result on the non-distortability of l_p and c₀, and establishing new classes of operator ideals.

Workshop in Analysis and Probability Seminar

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.