Abstract
Theorems due to Stenger (Bull Am Math Soc 74:369–372, 1968) and Nudelman (Int Equ Oper Theory 70:301–305, 2011) in Hilbert spaces and their generalizations to Krein spaces in Azizov and Dijksma (Int Equ Oper Theory 74(2):259–269, 2012) and Azizov et al. (Linear Algebra Appl 439:771–792, 2013) generate additional questions about properties a finite-codimensional compression \({T_0}\) of a symmetric or self-adjoint linear relation \({T}\) may or may not inherit from \({T}\). These questions concern existence of invariant maximal nonnegative subspaces, definitizability, singular critical points and defect indices.
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Dedicated to Heinz Langer with congratulations for his 80th birthday and the honorary doctorates from Stockholm University and the Technical University Dresden
The research of Tomas Azizov was supported by Grant RFBR 15-01-05315-a.
We have the sad task to inform the reader that our coauthor Tomas Yakovlevich Azizov died on January 23, 2016. He was an exceptionally creative mathematician, a highly valued close friend and a gentle person. We shall miss him.
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Azizov, T., Ćurgus, B. & Dijksma, A. Finite-Codimensional Compressions of Symmetric and Self-Adjoint Linear Relations in Krein Spaces. Integr. Equ. Oper. Theory 86, 71–95 (2016). https://doi.org/10.1007/s00020-016-2313-2
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DOI: https://doi.org/10.1007/s00020-016-2313-2