2015/09/30 by Konstantin A. Makarov, Stephan Schmitz, Albrecht Seelmann
Mathematics · #math.FA #math.SP #msc:47A15 #msc:47A55 #msc:47A62
paper · pdf · doi:10.1007/s00020-016-2297-y
published as Integral Equations and Operator Theory, 85(3), 399-425, 2016 · 21 pages. This paper provides a complete overhaul and extension to the authors previous work arXiv:1307.6439 and includes an example
arxiv created 2016/08/02 · arxiv updated 2016/08/03
In this paper we discuss the problem of decomposition for unbounded 2× 2 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.