School of Mathematics
Mathematics Course 321 - Functional Analysis
Exercise sheets
- Exercises 1 [Due Friday October 17th
2008.]
-
Basic metric space theory. (Bounded) (continuous) functions on a
finite set.
(There are also some comments on the
solutions to this sheet.)
- Exercises 2 [Due Monday November 10th.]
-
Facts on complete metrics, uniform continuity, Baire category.
(Some comments on the solutions.)
- Exercises 3 [Due Friday November 28th.]
-
Fact about little ell-p spaces and separability.
(Some comments on the solutions.)
- Exercises 4 [Due Monday January 12th.]
-
Practice with big-ell-p norms. Bounded linear operators as a new
space.
(Some comments on the solutions.)
- Exercises 5 [Due Friday January 30th.]
-
One exercise on the closed graph theorem. Partial orders and Zorn's lemma.
(Some comments on the solutions.)
- Exercises 6 [Due Friday February 13th.]
-
More on partial orders. Hamel bases.
(Some comments on the solutions.)
- Exercises 7 [Due Thursday March 5th.]
-
Norms on direct sums (of normed spaces); external versus internal
direct sum; dual of p-norm on direct sum is q-norm on direct sum
of duals; 2-norm on direct sum of Hilbert spaces gives a Hilbert
space.
(Some comments on the solutions.)
- Exercises 8 [Due Monday March 30th.]
-
Projections in Banach spaces and orhtogonal projections in Hilbert spaces.
(Some comments on the solutions.)
