Abstract
Consider an operator which is defined in Banach or Hilbert space X = X 1 × X 2 by the matrix \(L = \left( {\begin{array}{*{20}{c}}A&B \\ C&D \end{array}} \right)\), where the linear operators A: X 1 → X 1, B: X 2 → X 1, C: X 1 → X 2, and D: X 2 → X 2 are assumed to be unbounded. In the case when the operators C and B are relatively bounded with respect to the operators A and D, respectively, new conditions of closedness or closability are obtained for the operator L. For the operator L acting in a Hilbert space, analogs of Rellich–Kato theorems on the stability of self-adjointness are obtained.
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References
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Original Russian Text © A. A. Shkalikov, C. Trunk, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 6, pp. 932–938.
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Shkalikov, A.A., Trunk, C. On stability of closedness and self-adjointness for 2 × 2 operator matrices. Math Notes 100, 870–875 (2016). https://doi.org/10.1134/S0001434616110274
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DOI: https://doi.org/10.1134/S0001434616110274