Volumetric invariants and operators on random families of Banach spaces

Piotr Mankiewicz, and Nicole Tomczak-Jaegermann. "Volumetric invariants and operators on random families of Banach spaces." Studia Mathematica 159.2 (2003): 315-335. <http://eudml.org/doc/285217>.

@article{PiotrMankiewicz2003,
abstract = {The geometry of random projections of centrally symmetric convex bodies in $ℝ^\{N\}$ is studied. It is shown that if for such a body K the Euclidean ball $B₂^\{N\}$ is the ellipsoid of minimal volume containing it and a random n-dimensional projection $B = P_\{H\}(K)$ is “far” from $P_\{H\}(B₂^\{N\})$ then the (random) body B is as “rigid” as its “distance” to $P_\{H\}(B₂^\{N\})$ permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).},
author = {Piotr Mankiewicz, Nicole Tomczak-Jaegermann},
journal = {Studia Mathematica},
keywords = {Banach-Mazur distance; basis constant; convex body; finite-dimensional normed space; Gaussian quotients; mixing constant; mixing operators; random projections; rigidity; symmetry constant},
language = {eng},
number = {2},
pages = {315-335},
title = {Volumetric invariants and operators on random families of Banach spaces},
url = {http://eudml.org/doc/285217},
volume = {159},
year = {2003},
}

TY - JOUR
AU - Piotr Mankiewicz
AU - Nicole Tomczak-Jaegermann
TI - Volumetric invariants and operators on random families of Banach spaces
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 2
SP - 315
EP - 335
AB - The geometry of random projections of centrally symmetric convex bodies in $ℝ^{N}$ is studied. It is shown that if for such a body K the Euclidean ball $B₂^{N}$ is the ellipsoid of minimal volume containing it and a random n-dimensional projection $B = P_{H}(K)$ is “far” from $P_{H}(B₂^{N})$ then the (random) body B is as “rigid” as its “distance” to $P_{H}(B₂^{N})$ permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).
LA - eng
KW - Banach-Mazur distance; basis constant; convex body; finite-dimensional normed space; Gaussian quotients; mixing constant; mixing operators; random projections; rigidity; symmetry constant
UR - http://eudml.org/doc/285217
ER -