FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 641-650

V. Y. Protassov

Abstract

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```
We study an operation of generalized addition of convex bodies
(
```$p$ -addition, $p\in [1,+\infty]$ ), converting
the class of bounded symmetrical convex subsets of a normed linear
space into an Abelian subgroup with a natural action of
positive scalars on it.

We investigate properties of this operation and mention its
applications to the problem of computing of the joint spectral
radius of linear operators. We prove that
$p$ -addition is the unique associative operation
among some natural class of binary operations on the set
of symmetrical convex bodies.

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Last modified: June 17, 1998