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arXiv · 1509.07984

On invariant graph subspaces

Konstantin A. Makarov·Stephan Schmitz·Albrecht Seelmann
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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.

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Konstantin A. Makarov, Stephan Schmitz, Albrecht Seelmann. 2016-08-02. On invariant graph subspaces. https://doi.org/10.1007/s00020-016-2297-y

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