Functional analysis is the branch of mathematics concerned with the study of spaces of functions. Helemskii (Moscow State U., Russia) presents this text as an introduction to the field, devoting the bulk of it to the classical functional analysis of normed, Banach, and Hilbert spaces, but also covering polynormed spaces and some of their applications, as well as those elements of the theory of Banach algebras important to the study of spectra. The treatment differs from others on the same topic in that it emphasizes the categorical nature of the fundamental construction and results. The text assumes knowledge of linear algebra, the foundations of real analysis, and the elements of the theory of metric spaces found in advanced analysis courses. Annotation �2006 Book News, Inc., Portland, OR (booknews.com)

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