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.

Keywords: Operator matrix, positive operator, selfadjoint operator, spectrum.

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