## Functional Analysis Seminar 2005-2006

Here is the reading guide to Carother's book.

**Scans**

Scans of three pages of the first book by Lindenstrauss and Tzafriri (containing, amongst others, an insightful proof of the fact that the Haar system is a basis of L_p: page 1, page 2, page 3.

Scan of page 41 in Wojtaszczyk, containing a proof of the Principle of Small Perturbations showing that a small enough perturbation of a basis yields a basis again (and not just a basic sequence).

Scan of the proof of Corollary 5.7 in Carother's book as given on page 53 in the first book by Lindenstrauss and Tzafriri, as well as the pages containing their version and proof of the Principle of Small Perturbation (which is used): page 53, page 5, page 6.

**Homework assignments**

First assignment.

Second assignment.

Third assignment.

Fourth and final assignment.

Deadline: I will allow myself as many days to correct the work as you will allow yourself to work on it.