A. Castejon, E. Corbacho, V. Tarieladze

MD-Numbers and Asymptotic MD-Numbers of Operators

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.