Auslander–Reiten sequences are the central item of Auslander–Reiten theory, which is one of the most important techniques for the investigation of the structure of abelian categories.

The problem of$subextension$of plurisubharmonic functions is considered. Recently it was shown by Cegrell–Zeriahi, that subextension is always possible for negative plurisubharmonic functions in the energy class ℱ. In this paper we construct, for every hyperconvex domain Ω, a negative plurisubharmonic function in the class ℰ which cannot be subextended. Given any pseudoconvex domain we construct a pluriharmonic function that cannot be subextended.

We prove that the absolutely continuous subspace of the completely non-selfadjoint part of a first-order dissipative Dirac-like system is trivial when the imaginary part of the potential is non-integrable.

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In this paper, we generalize a theorem of Kallman [2, Theorem 1.1] and we resolve the unsettled case there.