Shizuo Kakutani

Shizuo Kakutani (角谷 静夫, Kakutani Shizuo, August 28, 1911 in Ōsaka – August 17, 2004 in New Haven, Connecticut) was a Japanese-American mathematician, best known for his eponymous fixed-point theorem.

Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. At one point he spent two years at the Institute for Advanced Study in Princeton at the invitation of the mathematician Hermann Weyl. While there, he also met John von Neumann.

Kakutani received his Ph.D. in 1941 from Osaka University^[1] and taught there through World War II. He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale in 1949, where he won a students choice award for excellence in teaching.^[2]

Kakutani received two awards of the Japan Academy, the Imperial Prize and the Academy Prize in 1982, for his scholarly achievements in general and his work on functional analysis in particular.

The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.

Kakutani's other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.

The Collatz conjecture is also known as the Kakutani conjecture.

His daughter, Michiko Kakutani, is a Pulitzer Prize-winning literary critic for the New York Times.

See also

• Kakutani fixed point theorem
• Kakutani's theorem (geometry)
• Kakutani–Rokhlin lemma

List of books available in English

• Selected papers / Shizuo Kakutani ; Robert R. Kallman, editor (1986)

References

External links

• New York Times obituary
• Obituary, University of Massachusetts newsletter
• Obituary, Yale Bulletin and Calendar
• Biography, University of St. Andrews/Turnbull
• The Lost Theorems of Kakutani