On invariant graph subspaces

Abstract

In this paper we discuss the problem of decomposition for unbounded $2\times 2$ 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.

21 pages. This paper provides a complete overhaul and extension to the authors previous work arXiv:1307.6439 and includes an example

References in corpus (2)

• On the existence of solutions to the operator Riccati equation and the tanΘtheorem
• Representation Theorems for indefinite quadratic forms without spectral gap

Cited by in corpus (3)

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• Solvability of the operator Riccati equation in the Feshbach case
• On a minimax principle in spectral gaps