{"product_id":"an-introduction-to-functional-analysis-hardback-9780521899642","title":"An Introduction to Functional Analysis (Hardback) 9780521899642","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Introduction to Functional Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAccessible text covering core functional analysis topics in Hilbert and Banach spaces, with detailed proofs and 200 fully-worked exercises.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJames C. Robinson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521899642, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 12 March 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e416 pages, 17 b\/w illus.  215 exercises\u003cbr\u003e23.5 x 15.6 x 2.6 cm, 0.69 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This is a beautifully written book, containing a wealth of worked examples and exercises, covering the core of the theory of Banach and Hilbert spaces. The book will be of particular interest to those wishing to learn the basic functional analytic tools for the mathematical analysis of partial differential equations and the calculus of variations.' Endre Suli, University of Oxford\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Preliminaries: 1. Vector spaces and bases\u003cbr\u003e 2. Metric spaces\u003cbr\u003e Part II. Normed Linear Spaces: 3. Norms and normed spaces\u003cbr\u003e 4. Complete normed spaces\u003cbr\u003e 5. Finite-dimensional normed spaces\u003cbr\u003e 6. Spaces of continuous functions\u003cbr\u003e 7. Completions and the Lebesgue spaces Lp(?)\u003cbr\u003e Part III. Hilbert Spaces: 8. Hilbert spaces\u003cbr\u003e 9. Orthonormal sets and orthonormal bases for Hilbert spaces\u003cbr\u003e 10. Closest points and approximation\u003cbr\u003e 11. Linear maps between normed spaces\u003cbr\u003e 12. Dual spaces and the Riesz representation theorem\u003cbr\u003e 13. The Hilbert adjoint of a linear operator\u003cbr\u003e 14. The spectrum of a bounded linear operator\u003cbr\u003e 15. Compact linear operators\u003cbr\u003e 16. The Hilbert–Schmidt theorem\u003cbr\u003e 17. Application: Sturm–Liouville problems\u003cbr\u003e Part IV. Banach Spaces: 18. Dual spaces of Banach spaces\u003cbr\u003e 19. The Hahn–Banach theorem\u003cbr\u003e 20. Some applications of the Hahn–Banach theorem\u003cbr\u003e 21. Convex subsets of Banach spaces\u003cbr\u003e 22. The principle of uniform boundedness\u003cbr\u003e 23. The open mapping, inverse mapping, and closed graph theorems\u003cbr\u003e 24. Spectral theory for compact operators\u003cbr\u003e 25. Unbounded operators on Hilbert spaces\u003cbr\u003e 26. Reflexive spaces\u003cbr\u003e 27. Weak and weak-* convergence\u003cbr\u003e Appendix A. Zorn's lemma\u003cbr\u003e Appendix B. Lebesgue integration\u003cbr\u003e Appendix C. The Banach–Alaoglu theorem\u003cbr\u003e Solutions to exercises\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Functional analysis \u0026amp; transforms [\u003ca title=\"See our other books on Functional analysis \u0026amp; transforms\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Functional%20analysis%20\u0026amp;%20transforms%20%5BPBKF%5D%22\"\u003ePBKF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004362608920,"sku":"9780521899642","price":78.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521899642i_c507e0b2-3fbd-4d4d-aed8-e17b6cbe0004.jpg?v=1691359185","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-introduction-to-functional-analysis-hardback-9780521899642","provider":"Freshly Printed Books","version":"1.0","type":"link"}