ON THE COMPLETENESS OF DERIVED CHAINS
Grigorii Vadimovich Radzievskii · Mathematics of the USSR-Sbornik · 1976
We study the problem of completeness of the system of eigenvectors and associated vectors of operator-valued functions which are analytic in an angular region and which assume values in the ring of bounded linear operators in a separable Hilbert space . As a corollary of the fundamental theorem proved in this paper we obtain the following result. Theorem 1. Let , where 0$ SRC=http://ej.iop.org/images/0025-5734/29/1/A04/tex_sm_3650_img4.gif/>, and is a completely continuous positive operator; moreover, let for some 0$ SRC=http://ej.iop.org/images/0025-5734/29/1/A04/tex_sm_3650_img8.gif/>. Then for every 0$ SRC=http://ej.iop.org/images/0025-5734/29/1/A04/tex_sm_3650_img9.gif/> the closed linear hull of the eigenvectors and associated vectors of (or ) which correspond to the eigenvalues lying in the angular region has finite defect in .Bibliography: 20 titles.