報告人：劉銳

報告題目：Bases, frames, and dilations of operator-valued measures on Banach spaces

時間：6月10日下午3點(diǎn)

地點(diǎn)：X2511

報告摘要：This talk is on the intersection topics between functional analysis and applied harmonic analysis: We introduce the concept of (Schauder) frames for Banach and operator spaces, show the connection with the bounded approximation property and complemented embedding, and give the duality theorems for frames and associated basis in reflexive Banach spaces. A general dilation theory of operator-valued measures and frames for Banach spaces is 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 our recent work, we show that every operator-valued system of imprimitivity with a projective isometric group representation has dilation to a spectral system of imprimitivity acting on a larger Banach space, and 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.

報告人簡介：劉銳，南開大學(xué)數(shù)學(xué)科學(xué)學(xué)院副教授，博士生導(dǎo)師 。研究方向：泛函分析，空間理論與應(yīng)用，論文發(fā)表在Memoirs of American Mathematical Society，Journal of Functional Analysis，F(xiàn)undamenta Mathematicae，Studia Mathematica等國際期刊，曾訪問美國德州大學(xué)奧斯汀分校、伊利諾伊大學(xué)香檳分校、德州農(nóng)工大學(xué)、中佛羅里達(dá)大學(xué)，主持國家自然科學(xué)基金面上項(xiàng)目，入選南開大學(xué)百名青年學(xué)科帶頭人培養(yǎng)計(jì)劃。

請各位老師和同學(xué)積極參加，尤其是泛函分析和調(diào)和分析方向的。