Maddox, Ivor J. Elements of functional analysis. 2. ed. (English) Zbl 0666.46003 Cambridge (UK) etc.: Cambridge University Press. xii, 242 p. £9.95/pbk; $ 22.95/pbk (1988). The following new topics are induced in the second edition [for the first ed. (1970) see Zbl 0193.08601]: 1. The Wiener algebra of absolutely convergent Fourier series. 2. Alaoglu’s theorem. 3. Differential and integral equations. 4. The Sturm-Liouville expansion theorem. 5. Revision of weak convergence and other topics. The appendix contans (i) the dual space of \(\ell_{\infty}\), (ii) the dual space of C[0,1], (iii) the Arzela-Ascoli theorem and (iv) the completeness of the Lebesgue integration space \(L_ p[0,1]\). Somewhat specialized topics, such as summability, Tauberian theorems, are not included in this edition. In the whole, the second edition retains its introductory character and clarity. This edition will be an ideal text for a first course in functional analysis. Reviewer: K.Chandrasekhara-Rao Cited in 44 Documents MSC: 46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 46B10 Duality and reflexivity in normed linear and Banach spaces 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) Keywords:Hahn-Banach theorem; Banach algebras; Hilbert space; Wiener algebra of absolutely convergent Fourier series; Alaoglu’s theorem; Differential and integral equations; Sturm-Liouville expansion theorem; weak convergence; Arzela-Ascoli theorem; completeness of the Lebesgue integration space Citations:Zbl 0193.08601 PDFBibTeX XMLCite \textit{I. J. Maddox}, Elements of functional analysis. 2. ed. Cambridge (UK) etc.: Cambridge University Press (1988; Zbl 0666.46003)