On Calkin's abstract symmetric boundary conditions (Q2849104)

The aim of the paper is to give an overview of \textit{J. W. Calkin}'s main results on reduction operators [Trans. Am. Math. Soc. 45, 369--442 (1939; Zbl 0021.13802)]. The authors note that the concept of a boundary triplet, widely known from the 1990's, can be considered as a bounded reduction operator with a suitable choice of the rotation operator, and they consider the more complicated unbounded case. Basic properties of reduction operators are given and are connected to unitary operators acting between Krein spaces and, hence, to unitary boundary triplets. A classification of reduction operators is introduced and characterized. Calkin's main results are reformulated using Krein space terminology and simplified proofs are included.NEWLINENEWLINEFor the entire collection see [Zbl 1269.47001].