Stable and Norm-stable Invariant Subspaces
Functional Analysis
2010-08-20 v2
Abstract
We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are the finite-dimensional ones. We also characterize norm-stable invariant subspaces of any weighted unilateral shift operator. We show that quasianalytic shift operators are points of norm continuity of the lattice of the invariant subspaces. We also provide a necessary condition for strongly stable invariant subspaces for certain operators.
Cite
@article{arxiv.1001.1018,
title = {Stable and Norm-stable Invariant Subspaces},
author = {Alexander Borichev and Don Hadwin and Hassan Yousefi},
journal= {arXiv preprint arXiv:1001.1018},
year = {2010}
}