| C-1 | The period we
called it the Local Theory, still a branch of Geometric Functional Analysis. [32]; [42]; [43]; [44]; [48]; [49]; [50]; [52]; [54]; [59]; [60]; [64]; [65]; [67]; [68]; [74]; [79]; [80]; [81]; [84]; Some crucial papers: |
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| [32] | 1971, see remarks in part A . | |
| [43] | 1977, joint with Figiel and Lindenstrauss; see remarks in part A | |
| [44] | 1978, joint with
Wolfson, - the extremal properties of l_1 is established. |
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| [49] | 1980, joint with Amir; see remarks in part A . | |
| [50] | 1981, joint with Davis and Tomczak-Jaegermann; | |
| [52] | 1982; joint with Alon; new combinatorial tools were brought to Local Theory. | |
| [54] | 1983; See [52] | |
| [60] | 1985, - The Quotient of a subspace theorem is proved; | |
| [65] | 1986, joint with Schechtman; see remarks in part A . | |
| [74] | 1986, joint with
Pisier; weak cotype and weak Hilbert spaces are introduced and studied. |
|
| [80] | 1987, joint with
Koenig; the duality of Entropy is established for operators of rank proportional to the dimension. . |
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| Related articles and books: Pisier, Gilles The volume of convex bodies and Banach space geometry. Cambridge Tracts in Mathematics, 94. Cambridge University Press, Cambridge, 1989. xvi+250 pp Tomczak-Jaegermann, Nicole Banach-Mazur distances and finite-dimensional operator ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics, 38. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. xii+395 pp |
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| C-2 | The change of
the point of view and the start of Asymptotic Geometric Analysis; (The use of Classical Convexity and Geometric Inequalities in Asymptotic Theory. Applications to Convexity) [57]; [58]; [66]; [71]; [72]; [73]; [76]; [78]; [82]; [83]; [85]; [87]; [88]; [89]; [90]; [91]; [92]; [94] --- [103]; [107] --- [120]; [122]; [123]; [124]; [126]; [127]; [128]; [130]; [131]; [132]; [134] --- [138]; [140]; [142] --- [148]. Some crucial papers: |
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| [57] | 1983/4, joint with Gromov; Brunn-Minkowski inequality is used first time in the Local Theory/Asymptotic Theory of Normed Spaces; generalization of Khinchine type inequality to arbitrary convex body. | |
| [58] | 1985; the paper introduced the theory of Geometric Inequalities to the Asymptotic study of Normed Spaces; it is a lecture delivered on L.Schwartz Colloquium at 1983; the publication of the volume was delayed for two years. | |
| [71] | 1985, joint with Bourgain; Reverse Blaschke-Santalo inequality and how to work with volumes in high dimension; the complete proofs are published in [78], 1987, | |
| [76] | 1986, - reverse Brunn-Minkowski ineq. is established. | |
| [82] | 1987, the first proved in the paper inequality contains a mistake, and should be corrected | |
| [85] | 1989, joint with Bourgain and Lindenstrauss; | |
| [87] | 1988, joint with Bourgain, Meyer and Pajor; very interesting inequality is under investigation; this was advanced very recently in [135] and [148] (both joint with Gluskin). | |
| [88] | 1988, relatively easy proofs of reverse Santalo and Brunn-Minkowski inequalities; there is not finsihed last part on mixed volume similar reverse inequality. | |
| [90] | 1988, joint with
Bourgain and Lindenstrauss; it contains a few
central results and develop a method of reducing a number of
terms in Minkowski sums; the main result on a number of steps
of Minkowski symmetrizations needed to approximate an
euclidean ball, was very recently improved, and brought to the final form by B.Klartag. The study was continued in [96] for Steiner symmetrizations. |
|
| [92] | 1989, joint with Pajor; notion of inertion ellipsoids were revived; detail study of isotropic positions and isotropic constants. | |
| C-3 | Results of
mostly Geometric Nature. [92]; [121]; [122]; [125]; [126]; [130]; [137]; [141]; [144]; Some crucial papers: |
|
| [92] | 1989, joint with Pajor; see remarks in part C-2. | |
| [121] | 1999, joint with Alesker and Dar, | |
| [122] | 2000, joint with Pajor, | |
| [125] | 2000, joint with Giannopoulos, | |
| [137] | 2003, joint with Bourgain and Klartag, | |
| [141] | 2003, joint with Klartag. | |
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