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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Volumetric invariants and operators on random families of Banach spaces

### Tom 159 / 2003

Studia Mathematica 159 (2003), 315-335 MSC: Primary 46B20. DOI: 10.4064/sm159-2-10

#### Streszczenie

The geometry of random projections of centrally symmetric convex bodies in ${ \mathbb R}^N$ is studied. It is shown that if for such a body $K$ the Euclidean ball $B_2^N$ is the ellipsoid of minimal volume containing it and a random $n$-dimensional projection $B=P_H(K)$ is “far” from $P_H(B_2^N)$ then the (random) body $B$ is as “rigid” as its “distance” to $P_H(B_2^N)$ permits. The result holds for the full range of dimensions $1 \le n \le \lambda N$, for arbitrary $\lambda \in (0,1)$.

#### Autorzy

• Piotr MankiewiczInstitute of Mathematics
00-956 Warszawa, Poland
e-mail
• Nicole Tomczak-JaegermannDepartment of Mathematical and Statistical Sciences
University of Alberta
Edmonton, Alberta