Most of the material should be accessible to mathematicians with a working knowledge of measure theory, complex analysis, and elementary functional analysis, whether or not they have studied operators on Hilbert space. For the second edition, Radjavi (mathematics and statistics, Dalhousie U.) and Rosenthal (mathematics, U. of Toronto) have corrected errors and added a chapter on subsequent developments. They have not added an index. Annotation (c) Book News, Inc., Portland, OR (booknews.com)