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The characteristic function of an operator knot in the quaternionic Hilbert space. (Russian) Zbl 0606.46051

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

Citations:

Zbl 0182.458
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