On invariant graph subspaces
Spectral Theory
2016-08-03 v2 Functional Analysis
Abstract
In this paper we discuss the problem of decomposition for unbounded operator matrices by a pair of complementary invariant graph subspaces. Under mild additional assumptions, we show that such a pair of subspaces decomposes the operator matrix if and only if its domain is invariant for the angular operators associated with the graphs. As a byproduct of our considerations, we suggest a new block diagonalization procedure that resolves related domain issues. In the case when only a single invariant graph subspace is available, we obtain block triangular representations for the operator matrices.
Cite
@article{arxiv.1509.07984,
title = {On invariant graph subspaces},
author = {Konstantin A. Makarov and Stephan Schmitz and Albrecht Seelmann},
journal= {arXiv preprint arXiv:1509.07984},
year = {2016}
}
Comments
21 pages. This paper provides a complete overhaul and extension to the authors previous work arXiv:1307.6439 and includes an example