Pugach, V. I. The characteristic function of an operator knot in the quaternionic Hilbert space. (Russian) Zbl 0606.46051 Funkts. Anal. 25, 116-128 (1985). In order to investigate a linear (over quaternionic field) bounded operator which is ”near” to a antiself-adjoint operator, the operator knot in quaternionic Hilbert space and the characteristic function of such operator knot have been introduced. Roughly speaking, a quaternionic Hilbert space is a (linear) inner product space over the quaternionic field for which the value of the inner product is in the quaternionic field. The usually Hilbert space is then identified with a subspace of a quaternionic Hilbert space. With this identification, the author succeeds in transfering many interesting results [for example, the operator knot and its characteristic function et al. given by M. S. Brodskij, Triangular and Jordan representations for linear operators (Russian) (1969; Zbl 0182.458)], into the quaternionic Hilbert space setting. Reviewer: Sun Shunhua MSC: 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 47D99 Groups and semigroups of linear operators, their generalizations and applications 47A45 Canonical models for contractions and nonselfadjoint linear operators 47A67 Representation theory of linear operators 47B50 Linear operators on spaces with an indefinite metric Keywords:operator knot; quaternionic Hilbert space; characteristic function Citations:Zbl 0182.458 PDFBibTeX XMLCite \textit{V. I. Pugach}, Funkts. Anal. 25, 116--128 (1985; Zbl 0606.46051)