Mathematician:Shizuo Kakutani

Mathematician

Japanese-American mathematician, best known for his Kakutani Fixed-Point Theorem.

Nationality

Japanese-American

History

• Born: August 28, 1911 in Ōsaka
• Died: August 17, 2004 in New Haven, Connecticut

Theorems and Definitions

• Kakutani Skyscraper

The term Kakutani's Theorem as used here has been identified as being ambiguous. If you are familiar with this area of mathematics, you may be able to help improve $\mathsf{Pr} \infty \mathsf{fWiki}$ by determining the precise term which is to be used. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Disambiguate}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

• Kakutani's Theorem
• Kakutani Fixed-Point Theorem
• Kakutani's Theorem (Geometry)

• Kakutani-Rokhlin Lemma (with Vladimir Abramovich Rokhlin)

• Birkhoff-Kakutani Theorem (with Garrett Birkhoff)
• Markov-Kakutani Fixed-Point Theorem (with Andrey Andreyevich Markov Jr.)
• Riesz-Markov-Kakutani Representation Theorem (with Frigyes Riesz and Andrey Andreyevich Markov Jr.)

Results named for Shizuo Kakutani can be found here.

Definitions of concepts named for Shizuo Kakutani can be found here.

Publications

• 1941: A generalization of Brouwer's fixed point theorem (Duke Math. J. Vol. 8, no. 3: pp. 457 – 459)
• 1941: Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem (Ann. Math. Vol. 42, no. 2: pp. 523 – 537)  www.jstor.org/stable/1968915
• 1941: Concrete representation of abstract $(M)$-spaces (A characterization of the space of continuous functions) (Ann. Math. Vol. 42, no. 4: pp. 994 – 1024)  www.jstor.org/stable/1968778
• 1948: On equivalence of infinite product measures (Ann. Math. Vol. 49, no. 1: pp. 214 – 224)  www.jstor.org/stable/1969123

Critical View

One day Shizuo Kakutani was teaching a class at Yale. He wrote down a lemma on the blackboard and announced that the proof was obvious. One student timidly raised his hand and said that it wasn't obvious to him. Could Kakutani explain?

After several moments' thought, Kakutani realized that he could not himself prove the lemma. He apologized, and said that he would report back at their next class meeting.

After class, Kakutani, went straight to his office. He labored for quite a time and found that he could not prove the pesky lemma. He skipped lunch and went to the library to track down the lemma. After much work, he finally found the original paper. The lemma was stated clearly and succinctly. For the proof, the author had written, 'Exercise for the reader.'

The author of this 1941 paper was Kakutani.

-- from Mathematical Apocrypha by Steven Krantz

Also known as

In Japanese: 角谷 静夫

Also rendered Kakutani Shizuo

Sources

• John J. O'Connor and Edmund F. Robertson: "Shizuo Kakutani": MacTutor History of Mathematics archive