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On multiple completeness of eigen-elements of some two-parametric system. (Russian. English summary) Zbl 0605.47015

The authors consider the two-parametric system \((A_{0i}+\lambda A_{1i}+\lambda^ 2A_{2i}+\mu A_{3i}+\mu^ 2A_{4i})x_ i=0\), \(i=1,2\), involving bounded linear operators \(A_{ji}\) acting in separable Hilbert spaces \(H_ i\) and show that this system possesses, under additional conditions on \(A_{ji}\), a two-fold complete system of eigenvectors of the form \(x_ 1\otimes x_ 2\in H_ 1\otimes_{\alpha}H_ 2\) (\(\alpha\) being an admissible uniform cross- norm).
Reviewer: J.Danesova

MSC:

47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47A10 Spectrum, resolvent
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