Functional analysis. (Q2724075)

The present book is a well organized introduction to functional analysis directed mainly to advanced undergraduate students of mathematics and may be used as an interesting addition by researchers in mathematical physics and engineering sciences. It consists of 29 chapters.NEWLINENEWLINENEWLINEIn chapters 1-10 the authors develop the necessary tools from linear algebra, metric spaces and topology, and introduce the reader to the main topic of this book: The Banach spaces and the Hilbert spaces.NEWLINENEWLINENEWLINEChapters 11-17 treat the celebrated Hahn-Banach theorem, the principle of uniform boundedness, and the closed graph theorem.NEWLINENEWLINENEWLINEIn chapters 18-23 are discussed spectral properties of linear operators and the reader can find here a condensed self-contained exposition of the Gelfand theory.NEWLINENEWLINENEWLINEChapters 23-28 offer several proofs of the spectral theorem for bounded, self-adjoint operators, and finally, the last chapter generalizes the preceeding results, removing boundedness from the hypothesis of the theorem.NEWLINENEWLINENEWLINE[For a review of the 1966 original see Zbl 0141.11502].