**A. Castejon, E. Corbacho, V. Tarieladze**

## MD-Numbers and Asymptotic MD-Numbers of Operators

**abstract:**

First, the basic properties of mean dilatation (MD-) numbers for
linear operators acting from a finite-dimensional Hilbert space are
investigated. Among other results, in terms of first and second order
MD-numbers, a characterization of isometries is obtained and a dimension-free
estimation of the $p$-th order MD-number by means of the first order
MD-number is established. After that asymptotic MD-numbers for a continuous
linear operator
acting from an infinite-dimensional Hilbert space are introduced and it is
shown that in the case of an infinite-dimensional domain
the asymptotic $p$-th order MD-number, rather unexpectedly, is simply the
$p$-th power of the asymptotic first order MD-number.