# AVERAGE DISTANCES AND OCTAHEDRAL NORMS

• Published : 1999.05.01

#### Abstract

In [6], Godefroy defined octahedral norms to give an isomorphic characterization of spaces containing $\ell_1$. Here we will show that such norms can be defined by using "average distances" as introduced in[1]. Also, we indicate some other properties of average distances : in particular, we give some estimates for their values in the product of two spaces, furnished with the max or the sum norm.

#### References

1. Atti Sem. Mat. Fis. Univ. Modena v.45 On the average distance property and the size of the unit sphere M. Baronti;E. Casini;P. L. Papini
2. Nonlinear Anal. to appear Average distances and the geometry of Banach spaces M. Baronti;E. Casini;P. L. Papini
3. Amer. Math. Monthly v.93 Numerical geometry - numbers for shapes J. Cleary;S. A. Morris;D. Yost
4. Smoothness and renormings in Banach spaces R. Deville;G. Godefroy;V. Zizler
5. Studia Math v.95 Metric characterization of first Baire class linear forms and octahedral norms G. Godefroy
6. Normes lisses et normes anguleuses sur les espaces de Banach separables G. Godefroy;B. Maurey
7. Arch. Math. v.68 The average distance property of Banach spaces P. K. Lin
8. Arch. Math. v.62 On the average distance property of spheres in Banach saces R. Wolf
9. Bull. Austral. Math. Soc. v.55 Averaging distances in certain Banach spaces R. Wolf
10. Bull. Austral. Math. Soc. v.26 Average distance in compact connected spaces D. Yost