Volumetric invariants and operators on random families of Banach spaces

• Autorzy: Piotr Mankiewicz , Nicole Tomczak-Jaegermann
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 2
• Strony: 315-335

Daty

wydano

2003

Twórcy

autor

Piotr Mankiewicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Nicole Tomczak-Jaegermann

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Identyfikatory

DOI

10.4064/sm159-2-10