We show that there are linear operators on Hilbert space that have n-dimensional subspaces with dense orbit, but no (n-1)-dimensional subspaces with dense orbit. This leads to a new class of operators, called the n-supercyclic operators. We show that many cohyponormal operators are n-supercyclic. Furthermore, we prove that for an n-supercyclic operator, there are n circles centered at the origin such that every component of the spectrum must intersect one of these circles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-3,
author = {Nathan S. Feldman},
title = {n-supercyclic operators},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {141-159},
zbl = {1006.47008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-3}
}
Nathan S. Feldman. n-supercyclic operators. Studia Mathematica, Tome 151 (2002) pp. 141-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-3/