4月1日

9:00-11:30

We begin the course introducing the notion of Schauder basis and   related topics. In this first talk we will start a detailed proof of   different characterizations for a sequence in a Banach space to be a Schauder   basis.

4月1日

14:00-16:30

In the second talk we will finish the proof initiated at the end   of Lecture 1 and we will introduce the notion of basic sequence, a sequence   which is a Schauder basis of its closed linear span.

4月2日

9:00-11:30

In this talk, we will finish the lecture with a historical review   of both concepts including some landmark results like the Banach--Mazur   theorem and the basis problem, solved by Enflo in 1973.

4月2日

14:00-16:30

In the this lecture we will introduce a special type of basis, the   so called unconditional bases, which play a central role in the theory of   bases. Examples and key theorems about them will be given, including the some   history of the unconditional basic sequence problem, solved by Gowers and   Maurey in 1993.

4月2日

18：30-20：00

Discussion

4月3日

9:00-11:30

We then turn to the classical sequence spaces L_p for 1 ≤ p < 1   . The techniques developed in the previous section will prove very useful in   this context. These Banach spaces are, in a sense, the simplest of all Banach   spaces, and their structure has been well understood

for many years.

4月3日

14:00-16:30

In the final lecture we will introduce the so-called greedy bases,   which is an active area of research nowadays. These bases are also important form   a practical point of view.