Read one of the following papers or (collections of papers and other sources). In five pages (or so) summarize the work and explain how it has effected further developments. In some cases, it may be more appropriate to discuss the work leading up to the assigned paper. Be prepared to demonstrate some central argument in the work.

MathSciNet is a good resource for understanding these paper's trace in the literature.

I can also suggest further references as needed.

1.Alspach

For this assignment, one should also use

either:

Maurey, B.

Points fixes des contractions de certains faiblement compacts de $L\sp{1}$.

47H10 (46B99 47H09)

or

Elton, J.(1-GAIT); Lin, Pei-Kee(1-TX); Odell, E.(1-TX); Szarek, S.(1-TX)

Remarks on the fixed point problem for nonexpansive maps.

Contemp. Math., 18,

47H10

2.Beckner

Far this assignment, one can also consult the final section of chapter 2 in Daniel Stroock's book

Probability Theory: An analytic viewpoint.

3.Beurling

4. Bourgain

5.CoifmanFefferman

6. Gelfand:

MR0026763

Gel

Normed rings with involutions and their representations.

46.3X

Gelfand, I.

Normierte Ringe. (German. Russian summary)

46.3X

Gelfand, I.

Über absolut konvergente trigonometrische Reihen und Integrale. (German. Russian summary)

See chapter 1 of

Gamelin, Theodore W.

Uniform algebras.

46J10 (30A98)

7.Korner

8.Lieb

9.Rudin:

Rudin, Walter

Trigonometric series with gaps.

42.00

See also

Bourgain, Jean(1-IASP-SM)

$\Lambda\sb p$-sets in analysis: results, problems and related aspects.

43A46 (11K99 42B25 46N99)

10.Stein

11.Strassen

12.Talagrand