Speaker: Jingbo Xia (SUNY at Buffalo)
Host: Huaxin Lin
Abstract: It is well known that Toeplitz operators on the Bergman space L^2_a(B) are localized in a well-defined sense, and this localization has applications. In contrast, recent examples show that Toeplitz operators on the Hardy space H^2(S) are generally not localized. We remedy this situation by developing a theory of localization on H^2(S). Specifically, we introduce a C^*-algebra L on H^2(S), and we show that the operators in L have all the right localization properties. Moreover, we show that this L is maximal with respect to these properties. As it turns out, L contains the Toeplitz operators with continuous symbols on H^2(S), but the proof of this fact is not easy. Finally, we apply our localization to solve a spectral-gap problem arising from the Arveson-Douglas conjecture.
Time: 14:30, Friday, Jun. 6, 2025
Location: R1410, SIMIS
Introduction to the speaker: Jingbo Xia is a professor in the Department of Mathematics at the University at Buffalo (SUNY at Buffalo). His research primarily focuses on operator theory, functional analysis, and mathematical physics. He has published papers in many top-tier journals, such as Trans. Amer. Math. Soc., Commun. Math. Phys., Adv. Math., etc.
English 
简体中文