Martin Ribe

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Martin G. Ribe (* 1945 ) is a Swedish mathematician who deals with functional analysis .

Ribe received his doctorate in 1972 from the University of Linköping under Hans Rådström (1919–1970) (On spaces which are not supposed to be locally convex). From 1972 to 1974 he was at the Mittag-Leffler Institute .

Ribe published only a few, but very influential, works on functional analysis. His main occupation was a statistician.

Ribe proved in 1976 that the linear structures of standardized spaces are preserved under uniform homeomorphisms. More precisely: if X, Y are uniformly homeomorphic Banach spaces, then they have the same finite dimensional subspaces. Their linear local structure is the same and should therefore be definable by purely metric properties without recourse to the linear structure. This rigidity theorem became the starting point of a program (Ribe program, so called by Jean Bourgain 1986), which applies the theorem to general metric spaces without linear structures in their definition and studies them with methods similar to the local theory of Banach spaces, with applications in Group theory, harmonic analysis and computer science.

Fonts

  • On uniformly homeomorphic normed spaces , Arkiv Math., Vol. 14, 1976, 237-244, Part 2, Vol. 16, 1978, 1-9
  • Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces , Pacific J. Math. 44, 1973, 715-732

Individual evidence

  1. ↑ After Radström's death, Edgar Asplund from Aarhus took over the supervision of the doctoral thesis
  2. ↑ Martin Ribe in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ↑ He achieved initial success in this direction by characterizing superreflective spaces via the Ribe program, Israel J. Math., 56, 1986, 222–230
  4. ↑ Assaf Naor An introduction to the Ribe Program , Japanese J. Math., 7, 2012, 167-233
  5. ↑ Keith Ball The Ribe Program , Séminaire Bourbaki, 1047, 2011/2012
personal data
SURNAME Ribe, Martin
ALTERNATIVE NAMES Ribe, Martin G.
BRIEF DESCRIPTION Swedish mathematician
DATE OF BIRTH 1945