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Orbituary: “Ky Fan (1914–2010), he spent every waking moment thinking about mathematics”. (English) Zbl 1282.01031

Summary: 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.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
47-03 History of operator theory
90-03 History of operations research and mathematical programming
49-03 History of calculus of variations and optimal control

Biographic References:

Fan, Ky
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[1] Aubin J P. Mathematical Methods of Games and Economic Theory. Amsterdam: North-Holland, 1979 · Zbl 0452.90093
[2] Aubin J P, Ekeland I. Applied Nonlinear Analysis. New York: JohnWiley & Sons, 1984 · Zbl 0641.47066
[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 · Zbl 0483.47038
[5] Fan K. On a theorem of Weyl concerning eigenvalues of linear transformations, I. Proc Nat Acad Sci USA, 1949, 35: 652–655 · doi:10.1073/pnas.35.11.652
[6] Fan K. On a theorem of Weyl concerning eigenvalues of linear transformations, II. Proc Nat Acad Sci USA, 1950, 36: 31–35 · Zbl 0041.00602 · doi:10.1073/pnas.36.1.31
[7] Fan K. Maximum properties and inequalities for the eigenvalues of completely continuous operators. Proc Nat Acad Sci USA, 1951, 37: 760–766 · Zbl 0044.11502 · doi:10.1073/pnas.37.11.760
[8] Fan K. Fixed-point and minimax theorems in locally convex topological linear spaces. Proc Nat Acad Sci USA, 1952, 38: 121–126 · Zbl 0047.35103 · doi:10.1073/pnas.38.2.121
[9] Fan K. Minimax theorems. Proc Nat Acad Sci USA, 1953, 39: 42–47 · Zbl 0050.06501 · doi:10.1073/pnas.39.1.42
[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 · Zbl 0072.37602
[11] Fan K. Topological proofs for certain theorems on matrices with non-negative elements. Monatsh Math, 1958, 62: 219–237 · Zbl 0081.25104 · doi:10.1007/BF01303967
[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 · Zbl 0099.31802
[13] Fan K. Invariant subspaces of certain linear operators. Bull Amer Math Soc, 1963, 69: 773–777 · Zbl 0118.10803 · doi:10.1090/S0002-9904-1963-11028-9
[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 · Zbl 0138.37401 · doi:10.1007/BF02052284
[16] Fan K. Simplicial maps from an orientable n-pseudomanifold onto Sm with the octahedral triangulation. J Combin Theory, 1967, 2: 588–602 · Zbl 0149.41302 · doi:10.1016/S0021-9800(67)80063-2
[17] Fan K. Extensions of two fixed point theorems of F. E. Browder. Math Z, 1969, 112: 234–240 · Zbl 0185.39503 · doi:10.1007/BF01110225
[18] Fan K. On local connectedness of locally compact Abelian groups. Math Ann, 1970, 187: 114–116 · Zbl 0185.07201 · doi:10.1007/BF01350176
[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 · Zbl 0236.47049
[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 · Zbl 0307.15005 · doi:10.1016/0024-3795(75)90056-7
[23] Fan K. Extension of invariant linear functional. Proc AMS, 1977, 66(1): 23–29 · Zbl 0391.46004 · doi:10.1090/S0002-9939-1977-0458111-8
[24] Fan K. Analytic functions of a proper contraction. Math Z, 1978, 160: 275–290 · Zbl 0455.47013 · doi:10.1007/BF01237041
[25] Fan K. Julia’s lemma for operators. Math Ann, 1979, 239: 241–245 · Zbl 0378.47004 · doi:10.1007/BF01351489
[26] Fan K. Pick-Julia theorems for operators. Math Z, 1979, 168: 23–34 · Zbl 0389.47004 · doi:10.1007/BF01214433
[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 · Zbl 0465.47017 · doi:10.1007/BF01215332
[30] Fan K. Evenly distributed subsets of S n and a combinatorial application. Pacific J of Math, 1982, 98(2): 323–325 · Zbl 0488.55002 · doi:10.2140/pjm.1982.98.323
[31] Fan K. Some aspects of the development of linear algebra in the last sixty years. Linear Algebra Appl, 1992, 162-164: 15–22 · Zbl 0748.15002 · doi:10.1016/0024-3795(92)90370-P
[32] Fan K. Operator-valued typically real functions. Proc Amer Math Soc, 1996, 124: 765–771 · Zbl 0852.47007 · doi:10.1090/S0002-9939-96-03002-X
[33] Fan K. Antipodal and fixed point theorems for sets in \(\mathbb{R}\)n bounded by a finite number of spheres. Advances in Appl Math, 1999, 22: 219–226 · Zbl 0940.55001 · doi:10.1006/aama.1998.0629
[34] Fan K, Fréchet M. Introduction à la topologie combinatoire. I. Initiation. Paris: Vubert, 1945 · Zbl 0061.39304
[35] Fan K, Glicksberg I, Hoffman A J. Systems of inequalities involving convex functions. Proc Amer Math Soc, 1957, 8: 617–622 · Zbl 0079.02002 · doi:10.1090/S0002-9939-1957-0087574-2
[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 · Zbl 0794.47033
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