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Weak Distances between Random Subproportional Quotients of ℓm1

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of n-dimensional quotients of ℓn21 is greater than or equal to [formula].
Rocznik
Strony
285--294
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
  • Institute of Mathematics Polish Academy of Sciences Sniadeckich 8 P.O. Box 21 00-956 Warszawa 10, Poland
Bibliografia
  • [BP] K. Ball and A. Pajor, Convex bodies with few faces, Proc. Amer. Math. Soc. 110 (1990), 225–231.
  • [G1] E. D. Gluskin, The diameter of Minkowski compactum roughly equals n, Funct. Anal. Appl. 15 (1981), 57–58.
  • [G2] E. D. Gluskin, Finite-dimensional analogues of spaces without bases, Dokl. Akad. Nauk SSSR 216 (1981), 1046–1050 (in Russian).
  • [LMOT] R. Latała, P. Mankiewicz, K. Oleszkiewicz and N. Tomczak-Jaegermann, Banach–Mazur distances and projections on subgaussian random polytopes, Discrete Comput. Geom. 38 (2007), 29–50.
  • [M1] P. Mankiewicz, Finite-dimensional Banach spaces with symmetry constant of order √ n, Studia Math. 79 (1984), 193–200.
  • [M2] P. Mankiewicz, Subspace mixing properties of operators in Rn with application to Gluskin spaces, Studia Math. 88 (1988), 51–67.
  • [M3] P. Mankiewicz, Compact groups of operators on subproportional quotients of lm 1 , Canad. J. Math. 52 (2000), 999–1017.
  • [MT1] P. Mankiewicz and N. Tomczak-Jaegermann, Geometry of families of random projections of symmetric convex bodies, Geom. Funct. Anal. 11 (2001), 1282–1326.
  • [MT2] P. Mankiewicz and N. Tomczak-Jaegermann, Quotients of finite-dimensional Banach spaces; random phenomena, in: Handbook of the Geometry of Banach Spaces, W. B. Johnson and J. Lindenstrauss (eds.), Vol. II, North-Holland, Amsterdam, 2003, 1201–1246.
  • [R] M. Rudelson, Estimates of the weak distance between finite-dimensional Banach spaces, Israel J. Math. 89 (1995), 189–204.
  • [S1] S. J. Szarek, The finite-dimensional basis problem with an appendix on nets of Grassmann manifolds, Acta Math. 151 (1983), 153–179.
  • [S2] S. J. Szarek, On the existence and uniqueness of complex structure and spaces with “few” operators, Trans. Amer. Math. Soc. 293 (1986), 339–353.
  • [T] N. Tomczak-Jaegermann, The weak distance between finite-dimensional Banach spaces, Math. Nachr. 119 (1984), 291–307.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bad72e07-9032-42d1-9751-051a9944cf61
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