Functional Analysis (SISSA Springer Series, 7)

Functional Analysis (SISSA Springer Series, 7)



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English | 2026 | ISBN-10: 3032244749 | 160 pages| Epub PDF (True) | 18 MB

Functional Analysis is based on the lecture notes of a Functional Analysis course taught for many years by Sandro Zagatti at SISSA (the International School for Advanced Studies, Trieste). Faithfully transcribed and typeset after his passing, the book preserves the clarity, structure, and pedagogical precision that defined his teaching. The text provides a rigorous and complete introduction to the fundamental concepts and methods of functional analysis, guiding readers from the study of metric and normed spaces to the more advanced theory of Banach and Hilbert spaces. It develops systematically the key results that underlie modern analysis—the Hahn–Banach theorem, the Baire category theorem, compact and weak topologies, dual spaces, compact operators, and reflexivity—together with the classical spaces of continuous functions, sequence spaces, and Lp spaces. Each topic is presented with careful attention to logical structure and with numerous worked examples that illustrate both abstract results and their applications. The exposition emphasizes conceptual understanding and the ability to reason independently, following a style that makes abstract notions accessible without compromising mathematical rigor. The volume also includes a rich collection of exercises, many drawn from Zagatti’s original written exams, offering readers a way to consolidate and test their understanding. The problems often require combining ideas from different chapters, encouraging synthesis rather than rote application.

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