Obstructions for uniform stability of C_0-semigroup
Functional Analysis
2010-04-13 v1
Abstract
Let T be a C_0-semigroup on X with generator A. We prove that if the abscissa of uniform boundedness of the resolvent A is non-negative then for each a non-decreasing function h:[0,\infty] -> [0,\infty], there are x' in X' and x in X such that integral from 0 to \infty of h(|< x',T(t)x)>| is equal to \infty. If Sp(A) contained a number from iR then such x may be taken in D(A^\infty).
Cite
@article{arxiv.1004.1916,
title = {Obstructions for uniform stability of C_0-semigroup},
author = {K. V. Storozhuk},
journal= {arXiv preprint arXiv:1004.1916},
year = {2010}
}
Comments
9 pages