Ondřej Kalenda (Uniwersytet Karola w Pradze) Topological methods in Banach spaces. Harmonogram wykładów: wt, 23.10: 12:15-15:00 (WS) śr, 24.10: 14:15-16:00 (602) czw, 25.10: 14:15-16:00 (711) Opis Banach spaces are an important tool in several areas of mathematics. This theory allows us to consider complicated objects (functions, sequences, operators) as points in a space with certain structure. There are several structures on Banach spaces - metric, geometrical, topological etc. In the present minicourse we will focus on the topological point of view. We will study various topologies on Banach spaces (norm, weak, weak* and general weak topologies) and the relationship of topological properties with other type of properties. In particular, we will discuss certain duality between Banach spaces and compact spaces, properties of weakly compact sets and related classes of Banach spaces.
