You may work with one or two partners but each student should turn in their own write up of the assignment.

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:

MR0659309 (83h:47041)
Maurey, B.
Points fixes des contractions de certains faiblement compacts de $L\sp{1}$. (French) [Fixed points of the contractions of certain weakly compact subsets of $L\sp{1}$] Seminar on Functional Analysis, 1980--1981, Exp. No. VIII, 19 pp., École Polytech., Palaiseau, 1981.
47H10 (46B99 47H09)

or

MR0728595 (85d:47059)
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. Fixed points and nonexpansive mappings (Cincinnati, Ohio, 1982), 87--120,
Contemp. Math., 18, Amer. Math. Soc., Providence, RI, 1983.
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 (10,199a)
Gelʹfand, I. M.; Naĭmark, M. A.
Normed rings with involutions and their representations. (Russian)
Izvestiya Akad. Nauk SSSR. Ser. Mat. 12, (1948). 445--480.
46.3X
MR0004726 (3,51f)
Gelfand, I.
Normierte Ringe. (German. Russian summary)
Rec. Math. [Mat. Sbornik] N. S. 9 (51), (1941). 3--24.
46.3X
MR0004727 (3,51g)
Gelfand, I.
Über absolut konvergente trigonometrische Reihen und Integrale. (German. Russian summary)
Rec. Math. [Mat. Sbornik] N. S. 9 (51), (1941). 51--66.

See chapter 1 of

MR0410387 (53 #14137)
Gamelin, Theodore W.
Uniform algebras. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. xiii+257 pp.
46J10 (30A98)


7.Korner

8.Lieb

9.Rudin:
MR0116177 (22 #6972)
Rudin, Walter
Trigonometric series with gaps.
J. Math. Mech. 9 1960 203--227.
42.00
See also
MR1863693 (2003e:43006)
Bourgain, Jean(1-IASP-SM)
$\Lambda\sb p$-sets in analysis: results, problems and related aspects. Handbook of the geometry of Banach spaces, Vol. I, 195--232, North-Holland, Amsterdam, 2001.
43A46 (11K99 42B25 46N99)

10.Stein

11.Strassen

12.Talagrand