Block operator matrices are those with entries that are linear operators between Banach or Hilbert spaces, and appear in several areas of mathematics and its applications, explains Tretter (U. of Bern, Switzerland), and it is vitally important to know their spectral properties, which govern the time evolution and hence stability of the underlying physical systems as well as other crucial matters. She describes methods for investigating these spectral properties, emphasizing several classes of block matrix operators that do not yield themselves lightly to standard methods of operator theory. Her topics include localizing the spectrum and investigating its structure, characterizing and estimating eigenvalues, and applications to concrete problems from mathematical physics. Distributed in the US by World Scientific. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)