Isaac Namioka

Isaac Namioka

Isaac Namioka (born April 25, 1928)^[1] is a Japanese-American mathematician who has worked in general topology and functional analysis. He is a professor emeritus of mathematics at the University of Washington.^[2]

Early life and education

Namioka was born in Tōno, not far from Namioka in the north of Honshu, Japan. When he was young his parents moved farther south, to Himeji.^[3] He attended graduate school at the University of California, Berkeley, earning a doctorate in 1956 under the supervision of John L. Kelley.^[4] As a graduate student, Namioka married Chinese-American mathematics student Lensey Namioka, later to become a well-known novelist who used Namioka's Japanese heritage in some of her novels.^[3]

Career

Namioka taught at Cornell University until 1963, when he moved to the University of Washington.^[1] There he was the doctoral advisor to four students. He has over 20 academic descendants, largely through his student Joseph Rosenblatt, who became a professor at the University of Illinois at Urbana–Champaign.^[4]

Contributions

Namioka's book Linear Topological Spaces with Kelley has become a "standard text".^[1] However, although his doctoral work and this book both concerned general topology, his interests later shifted to functional analysis.^[5]

With Asplund in 1967, Namioka gave one of the first complete proofs of the Ryll-Nardzewski fixed-point theorem.^[6]

Following his 1974 paper "separate continuity and joint continuity", a Namioka space has come to mean a topological space X with the property that whenever Y is a compact space and function f from the Cartesian product of X and Y to Z is separately continuous in X and Y, there must exist a dense G_δ set within X whose Cartesian product with Y is a subset of the set of points of continuity of f.^[7][8] The result of the 1974 paper, a proof of this property for a specific class of topological spaces, has come to be known as Namioka's theorem.^[9]

In 1975, Namioka and Phelps established one side of the theorem that a space is an Asplund space if and only if its dual space has the Radon–Nikodým property. The other side was completed in 1978 by Stegall.^[10]

Awards and honors

A special issue of the Journal of Mathematical Analysis and Applications was dedicated to Namioka to honor his 80th birthday.^[1] In 2012, he became one of the inaugural fellows of the American Mathematical Society.^[11]

Selected publications

Books

• Partially Ordered Linear Topological Spaces (Memoirs of the American Mathematical Society 14, 1957)^[12]
• Linear Topological Spaces (with John L. Kelley, Van Nostrand, 1963; Graduate Texts in Mathematics 36, Springer-Verlag, 1976)^[13][14]

Research papers

• Namioka, I.; Asplund, E. (1967), "A geometric proof of Ryll-Nardzewski's fixed point theorem", Bulletin of the American Mathematical Society, 73: 443–445, MR 0209904, doi:10.1090/s0002-9904-1967-11779-8 .
• Namioka, I. (1974), "Separate continuity and joint continuity", Pacific Journal of Mathematics, 51: 515–531, MR 0370466, doi:10.2140/pjm.1974.51.515 .
• Namioka, I.; Phelps, R. R. (1975), "Banach spaces which are Asplund spaces", Duke Mathematical Journal, 42 (4): 735–750, MR 0390721, doi:10.1215/s0012-7094-75-04261-1 .

References