Ky Fan (1914-2010), he spent every waking moment thinking about mathematics

Abstract

This survey article on Dr. Ky Fan summarizes his versatile achievements and fundamental contributions in the fields of topological groups, nonlinear and convex analysis, operator theory, linear algebra and matrix theory, mathematical programming, and approximation theory, etc., and as well reveals Fan’s exemplary mathematical formation opening up the beauty of pure mathematics, with natural conditions, concise statements and elegant proofs. This article contains a brief biography of Dr. Fan and epitomizes his life. He was not only a great mathematician, but also a very serious teacher known to be extremely strict to his students. He loved his motherland and made generous donations for promoting mathematical development in China. He devoted his life to mathematics, continued his research and published papers till 85 years old.

Key words： Ky Fan; topological group; nonlinear and convex analysis; fixed point theory; operator theory; linear algebra and matrix theory; nonlinear programming; complex analysis; combinatory; approximation theory

References

1 Aubin J P. Mathematical Methods of Games and Economic Theory. Amsterdam: North-Holland, 1979

2 Aubin J P, Ekeland I. Applied Nonlinear Analysis. New York: JohnWiley & Sons, 1984

3 Dieudonne J. A Panorama of Pure Mathematics. As seen by N. Bourbaki. New York: Academic Press, 1982

4 Dugundji J, Granas A. Fixed Point Theory, I. Warszawa: PWM-Polish Scientific Publishers, 1982

5 Fan K. On a theorem of Weyl concerning eigenvalues of linear transformations, I. Proc Nat Acad Sci USA, 1949, 35: 652-655

6 Fan K. On a theorem of Weyl concerning eigenvalues of linear transformations, II. Proc Nat Acad Sci USA, 1950, 36: 31-35

7 Fan K. Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc Nat Acad Sci USA, 1951, 37: 760-766

8 Fan K. Fixed-point and minimax theorems in locally convex topological linear spaces. Proc Nat Acad Sci USA, 1952, 38: 121-126

9 Fan K. Minimax theorems. Proc Nat Acad Sci USA, 1953, 39: 42-47

10 Fan K. On systems of linear inequalities. In: Kuhn H W, Tuker A W, eds. Linear Inequalities and Related Systems. Annals of Math Studies, No 38. Princeton: Princeton Univ Press, 1956, 99-156

11 Fan K. Topological proofs for certain theorems on matrices with non-negative elements. Monatsh Math, 1958, 62: 219-237

12 Fan K. Linear inequalities and closure properties in normed linear spaces. In: Seminar on Analytic Functions, Vol. 2. Inst for Advanced Study, Princeton, 1958, 202-212

13 Fan K. Invariant subspaces of certain linear operators. Bull Amer Math Soc, 1963, 69: 773-777

14 Fan K. Invariant subspaces for a semigroup of linear operators. Proc Koninkl Nederl Akademle Van Wetenschappen—Amsterdam Ser A, 1965, 68(3): 447-451; also in: Indag Math, 1965, 27(3): 447-451

15 Fan K. Applications of a theorem concerning sets with convex sections. Math Ann, 1966, 163: 189-203; also in: Contributions to Functional Analysis. New York: Springer, 1966

16 Fan K. Simplicial maps from an orientable n-pseudomanifold onto S^m with the octahedral triangulation. J Combin Theory, 1967, 2: 588-602

17 Fan K. Extensions of two fixed point theorems of F. E. Browder. Math Z, 1969, 112: 234-240

18 Fan K. On local connectedness of locally compact Abelian groups. Math Ann, 1970, 187: 114-116

19 Fan K. A minimax inequality and applications. In: Shisha O, ed. Inequalities III. Proceedings of the Third Symposium on Inequalities. New York: Academic Press Inc, 1972, 103-113

20 Fan K. Covering properties of convex sets and fixed point theorems in topological vector spaces. In: Anderson R D, ed. Symposium on Infinite Dimensional Topology. Annals of Math Studies, No. 69. Princeton: Princeton Univ Press, 1972, 79-92

21 Fan K. Fixed-point theorems in functional analysis (supplementary manual for recording of a lecture). Audio Recording of Mathematical Lectures, 46. Providence: Amer Math Soc, 1972 (7 pages)

22 Fan K. Two applications of a consistency theorem for systems of linear inequalities. Linear Algebra Appl, 1975, 11: 171-180

23 Fan K. Extension of invariant linear functional. Proc AMS, 1977, 66(1): 23-29

24 Fan K. Analytic functions of a proper contraction. Math Z, 1978, 160: 275-290

25 Fan K. Julia’s lemma for operators. Math Ann, 1979, 239: 241-245

26 Fan K. Pick-Julia theorems for operators. Math Z, 1979, 168: 23-34

27 Fan K. Schwarz’s lemma for operators on a Hilbert space. Analeptic stintifice ale Universitatii “Al I. Cuza” Iasi Supliment la tomul XXV, s. I a, 1979

28 Fan K. A further generalization of Shapley’s generalization of the KKM theorem. In: Mosechlin O, Pallaschke D, eds. Game Theory and Mathematical Economics. Amsterdam: North Holland Publishing Company, 1981, 275-279

29 Fan K. Iteration of analytic functions of operators. Math Z, 1982, 179: 293-298

30 Fan K. Evenly distributed subsets of Sⁿ and a combinatorial application. Pacific J of Math, 1982, 98(2): 323-325

31 Fan K. Some aspects of the development of linear algebra in the last sixty years. Linear Algebra Appl, 1992, 162-164: 15-22

32 Fan K. Operator-valued typically real functions. Proc Amer Math Soc, 1996, 124: 765-771

33 Fan K. Antipodal and fixed point theorems for sets in ℝn bounded by a finite number of spheres. Advances in Appl Math, 1999, 22: 219-226

34 Fan K, Fréchet M. Introduction à la topologie combinatoire. I. Initiation. Paris: Vubert, 1945

35 Fan K, Glicksberg I, Hoffman A J. Systems of inequalities involving convex functions. Proc Amer Math Soc, 1957, 8: 617-622

36 Lim B-L. In Memoriam Professor Ky Fan (1914-2010). Preprint

37 Rockafellar R T. Convex Analysis. Princeton: Princeton Univ. Press, 1970

38 Stopple J. Dr. Fan, World Renowned Mathematician, Professor Emeritus of UC Santa Barbara. Preprint

39 Zeidler E. Nonlinear Functional Analysis and Its Applications, I-IV. Berlin: Springer-Verlag, 1993