Volume Ratio and Other s-Numbers of Operators Related to Local Properties of Banach Spaces

Abstract Volume ratio numbers are studied and inequalities relating them to other s-numbers of operators are established. Characterizations of spaces of weak cotype 2 in terms of s-numbers and of operator ideal norms are obtained.

[1]  Gaussian Processes and Mixed Volumes , 1987 .

[2]  Nicole Tomczak-Jaegermann,et al.  Projections onto Hilbertian subspaces of Banach spaces , 1979 .

[3]  V. Milman,et al.  Asymptotic Theory Of Finite Dimensional Normed Spaces , 1986 .

[4]  V. Milman,et al.  Random subspaces of proportional dimension of finite dimensional normed spaces: Approach through the isoperimetric inequality , 1985 .

[5]  E. Gluskin.  NORMS OF RANDOM MATRICES AND WIDTHS OF FINITE-DIMENSIONAL SETS , 1984 .

[6]  Gilles Pisier,et al.  Holomorphic semi-groups and the geometry of Banach spaces , 1982 .

[7]  T. Figiel,et al.  The dimension of almost spherical sections of convex bodies , 1976 .

[8]  Joram Lindenstrauss,et al.  Classical Banach spaces , 1973 .

[9]  N. Tomczak-Jaegermann.  Banach-Mazur distances and finite-dimensional operator ideals , 1989 .

[10]  A. Pajor,et al.  Sections of the unit ball of Ipn , 1988 .

[11]  G. Pisier.  Weak Hilbert Spaces , 1988 .

[12]  V. Milman,et al.  Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space , 1985 .

[13]  V. Milman,et al.  New volume ratio properties for convex symmetric bodies in ℝn , 1987 .

[14]  C. Schütt,et al.  Geometric and probabilistic estimates for entropy and approximation numbers of operators , 1987 .

[15]  R. Dudley.  The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes , 1967 .

[16]  Alain Pajor,et al.  Gelfand Numbers and Euclidean Sections of Large Dimensions , 1990 .

[17]  Andrej Yu. Garnaev,et al.  On widths of the Euclidean Ball , 1984 .

[18]  Gilles Pisier,et al.  Banach spaces with a weak cotype 2 property , 1986 .

[19]  Nicole Tomczak-Jaegermann,et al.  On nearly euclidean decomposition for some classes of Banach spaces , 1980 .

[20]  B. Carl.  Entropy numbers, s-numbers, and eigenvalue problems , 1981 .

[21]  Dualité des nombres d'entropie pour des opérateurs à valeurs dans un espace de Hilbert , 1987 .

[22]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[23]  Quotient Volumique et Espaces de Banach de Type 2 Faible , 1987 .

[24]  J. Vaaler.  A geometric inequality with applications to linear forms , 1979 .

[25]  C. Schütt.  Entropy numbers of diagonal operators between symmetric Banach spaces , 1984 .

[26]  B. Carl.  Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces , 1985 .