@article{JMAG_2013_9_1_a2,
author = {T. Oikhberg and M. I. Ostrovskii},
title = {Dependence of {Kolmogorov} {Widths} on the {Ambient} {Space}},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {25--50},
year = {2013},
volume = {9},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_1_a2/}
}
T. Oikhberg; M. I. Ostrovskii. Dependence of Kolmogorov Widths on the Ambient Space. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 1, pp. 25-50. http://geodesic.mathdoc.fr/item/JMAG_2013_9_1_a2/
[AO10] A. Aksoy, T. Oikhberg, “Some Results on Metric Trees”, Banach Algebras 2009, Banach Center Publ., 91, Polish Acad. Sci. Inst. Math., Warsaw, 2010, 9–34 | DOI | MR | Zbl
[AFS00] J. Appell, S. Franchetti, E. Semenov, “Estimates for the Jung Constant in Banach Lattices”, Israel J. Math., 116 (2000), 171–187 | DOI | MR | Zbl
[Bal87] K. Ball, “Inequality and Space-Packing in $l_p$”, Israel J. Math., 59 (1987), 243–256 | DOI | MR
[Bou81] J. Bourgain, New Classes of $\mathcal{L}^{p}$-spaces, Lect. Notes Math., 889, Springer-Verlag, Berlin–New York, 1981 | MR | Zbl
[CS90] B. Carl, I. Stephani, Entropy, Compactness, and the Approximation of Operators, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl
[Dav77] W. J. Davis, “A Characterization of $P_1$ spaces”, J. Approx. Theory, 21:4 (1977), 315–318 | DOI | MR | Zbl
[DJT95] J. Diestel, H. Jarchow, A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, Cambridge, 1995 | MR
[Dol87] Math. Notes, 42:4 (1987), 787–791 | DOI | MR | Zbl
[FLM77] T. Figiel, J. Lindenstrauss, V. Milman, “The Dimension of Almost Spherical Sections of Convex Bodies”, Acta Math., 139:1–2 (1977), 53–94 | DOI | MR | Zbl
[FS98] St. Petersburg Math. J., 10:5 (1999), 861–878 | MR | Zbl
[GG84] Soviet Math. Dokl., 30:1 (1984), 200–204 | MR | Zbl
[Glu81] Functional Anal. Appl., 15:1 (1981), 57–58 | DOI | MR | Zbl
[Ism74] Russian Math. Surveys, 29:3 (1974), 169–186 | DOI | MR | Zbl
[KS71] Math. Notes, 10 (1971), 694–696 | DOI | MR | Zbl
[Kas77] Math. USSR-Izv., 11:2 (1977), 317–333 (1978) | DOI | MR | Zbl | Zbl
[Koc90] Math. Notes, 48 (1990), 647–652 | DOI | MR | Zbl
[Kol36] A. Kolmogoroff, “Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse”, Ann. Math., 37 (1936), 107–111 | DOI | MR
[KKM48] M. G. Krein, M. A. Krasnoselskii, D. P. Milman, “On the Defect Numbers of Linear Operators in a Banach Space and on Some Geometric Questions”, Sb. Trudov Inst. Matem. AN USSR, 11, 1948, 97–112 (Russian)
[LL66] A. Lazar, J. Lindenstrauss, “On Banach Spaces Whose Duals are $L_1$ Spaces”, Israel J. Math., 4 (1966), 205–207 | DOI | MR | Zbl
[LP68] J. Lindenstrauss, A. Pełczyński, “Absolutely Summing Operators in $\mathcal{L}_{p}$-spaces and Their Applications”, Studia Math., 29 (1968), 275–326 | MR | Zbl
[LT73] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, Springer-Verlag, Berlin, 1973 | MR | Zbl
[LT79] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, v. II, Springer-Verlag, Berlin, 1979 | MR
[LPT06] A. Litvak, A. Pajor, N. Tomczak-Jaegermann, “Diameters of Sections and Coverings of Convex Bodies”, J. Funct. Anal., 231 (2006), 438–457 | DOI | MR | Zbl
[LGM96] G. G. Lorentz, M. V. Golitschek, Y. Makovoz, Constructive Approximation. Advanced Problems, Grundlehren der Mathematischen Wissenschaften, 304, Springer-Verlag, Berlin, 1996 | DOI | MR | Zbl
[MT03] P. Mankiewicz, N. Tomczak-Jaegermann, “Quotients of Finite Dimensional Banach Spaces; Random Phenomena”, Handbook of the Geometry of Banach Spaces, v. 2, North Holland, Amsterdam, 2003, 1201–1246 | DOI | MR | Zbl
[MP81] M. Marcus, G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Princeton Univ. Press, Princeton, 1981 | MR | Zbl
[MS86] V. D. Milman, G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Springer-Verlag, Berlin, 1986 | MR | Zbl
[Nac50] L. Nachbin, “A Theorem of the Hahn–Banach Type for Linear Transformations”, Trans. Amer. Math. Soc., 68:1 (1950), 28–46 | DOI | MR | Zbl
[Oik95] T. Oikhberg, “Absolute Widths of Some Embeddings”, J. Approx. Theory, 81:1 (1995), 120–126 | DOI | MR | Zbl
[Ost10] M. I.`Ostrovskii, “Asymptotic Properties of Kolmogorov Widths”, Bull. Aust. Math. Soc., 82:1 (2010), 10–17 | DOI | MR | Zbl
[OS09] M. I. Ostrovskii, V. S. Shulman, “Weak Operator Topology, Operator Ranges and Operator Equations via Kolmogorov Widths”, Integral Equations Operator Theory, 65 (2009), 551–572 | DOI | MR | Zbl
[Paj99] A. Pajor, “Metric Entropy of the Grassmann Manifold”, Convex Geometric Analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, 1999, 181–188 | MR | Zbl
[Pic88] Math. Notes, 43 (1988), 348–354 | DOI | MR | Zbl
[Pie80] A. Pietsch, Operator Ideals, North-Holland Mathematical Library, 20, North-Holland Publishing Co., Amsterdam–New York, 1980 | MR | Zbl
[Pie87] A. Pietsch, Eigenvalues and $s$-numbers, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl
[Pin85] A. Pinkus, $n$-widths in the Approximation Theory, Springer-Verlag, Berlin, 1985 | MR
[Pis82] G. Pisier, “Holomorphic Semigroups and the Geometry of Banach Spaces”, Ann. Math. (2), 115 (1982), 375–392 | DOI | MR | Zbl
[Pis83] G. Pisier, “Counterexamples to a Conjecture of Grothendieck”, Acta Math., 151:3–4 (1983), 181–208 | DOI | MR | Zbl
[Pis86] G. Pisier, “Factorization of Linear Operators and Geometry of Banach Spaces”, Published for the Conference Board of the Mathematical Sciences, Washington, DC, CBMS Regional Conference Series in Mathematics, 60, Amer. Math. Soc., Providence, RI, 1986 | MR
[Pis89] G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl
[Sza78] S. J. Szarek, “On Kashin's Almost Euclidean Orthogonal Decomposition of $\ell\sp{1}\sb{n}$”, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 26:8 (1978), 691–694 | MR | Zbl
[Sza81] S. J. Szarek, “Nets of Grassman Manifold and Orthogonal Group”, Proceedings of Research Workshop on Banach Space Theory (1981, Iowa City, Iowa), Univ. Iowa, Iowa City, IA, 1982, 169–185 | MR | Zbl
[Sza86] S. J. Szarek, “On the Existence and Uniqueness of Complex Structure and Spaces with “Few” Operators”, Trans. Amer. Math. Soc., 293:1 (1986), 339–353 | MR | Zbl
[Sza90] S. J. Szarek, “Spaces with Large Distances to $\ell_\infty^n$ and Random Matrices”, Amer. J. Math., 112:6 (1990), 899–942 | DOI | MR | Zbl
[ST80] S. J. Szarek, N. Tomczak-Jaegermann, “On Nearly Euclidean Decomposition for Some Classes of Banach Spaces”, Compositio Math., 40:3 (1980), 367–385 | MR | Zbl
[Tik60] Russian Math. Surveys, 15:3 (1960), 75–111 | DOI | MR | Zbl
[Tom89] N. Tomczak-Jaegermann, Banach–Mazur Distances and Finite-Dimensional Operator Ideals, Longman Scientific and Technical, Harlow, 1989 | MR
[Zip81a] M. Zippin, “The Range of a Projection of Small Norm in $\ell_1^n$”, Israel J. Math., 39 (1981), 349–358 | DOI | MR | Zbl
[Zip81b] M. Zippin, “The Finite Dimensional $P_\lambda$-spaces with Small $\lambda$”, Israel J. Math., 39 (1981), 359–364 | DOI | MR | Zbl
[Zip84] M. Zippin, “Errata to the paper "The Finite Dimensional $P_\lambda$-spaces with Small $\lambda$"”, Israel J. Math., 48 (1984), 255–256 | DOI | MR | Zbl
[Zip00] M. Zippin, “Orthogonal Almost Locally Minimal Projections on $\ell^n_1$”, Israel J. Math., 115 (2000), 253–268 | DOI | MR | Zbl