Journal of Operator Theory

Volume 33, Issue 2, Spring 1995 pp. 299-315.

On the spectra of the positive completions for operator matrices

Authors: Jin-Chuan Hou
Author institution: Department of Mathematics, Shanxi Teachers University, Linfen, Shanxi 041004, P.R. CHINA

Summary: Let A and B be positive (or selfadjoint) operators on Hilbert spaces

$\mathcal H$ and

$\mathcal K$ , respectively. In this paper, the union and the intersection of spectra of all positive (or Hermitian) completions of the partially specified operator matrix \left( {

$\begin{array}{*{20}c} A & ? \\ ? & B \\ \end{array}$ } \right) are completely characterized.

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