{"product_id":"a-first-course-in-functional-analysis-9780470146194","title":"A First Course in Functional Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis straight-forward, concise book is made up of carefully selected topics and is written in an accessible that requires minimal background knowledge. It provides the reader with a sense of unity in the subject's development and fully explains the essential concepts, outlining the logic behind the steps to familiarize the reader with the theories.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Graduate and advanced undergraduate students in mathematics and physics will appreciate this book as a useful and stimulating contribution to the vast array of textbooks on the subject..\" (Zentralblatt MATH, October 2010)\u003cbr\u003e \u003cbr\u003e   \u003cp\u003e\"\u003ci\u003eA First Course in Functional Analysis\u003c\/i\u003e is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2009c)\u003c\/p\u003e \u003cp\u003e\"It is written in a very open, nontelegraphic style, and takes care to explain topics as they come up.  Recommended.\" (\u003ci\u003eCHOICE\u003c\/i\u003e Oct 2008)\u003c\/p\u003e \u003cp\u003e\"This is an excellent text for reaching students of diverse backgrounds and majors, as well as scientists from other disciplines (physics, economics, finance, and engineering) who want an introduction to functional analysis.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e Oct 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Linear Spaces and Operators 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Linear Spaces 2\u003c\/p\u003e \u003cp\u003e1.3 Linear Operators 5\u003c\/p\u003e \u003cp\u003e1.4 Passage from Finite- to Infinite-Dimensional Spaces 7\u003c\/p\u003e \u003cp\u003eExercises 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Normed Linear Spaces: The Basics 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Metric Spaces 11\u003c\/p\u003e \u003cp\u003e2.2 Norms 12\u003c\/p\u003e \u003cp\u003e2.3 Space of Bounded Functions 18\u003c\/p\u003e \u003cp\u003e2.4 Bounded Linear Operators 19\u003c\/p\u003e \u003cp\u003e2.5 Completeness 21\u003c\/p\u003e \u003cp\u003e2.6 Comparison of Norms 30\u003c\/p\u003e \u003cp\u003e2.7 Quotient Spaces 31\u003c\/p\u003e \u003cp\u003e2.8 Finite-Dimensional Normed Linear Spaces 34\u003c\/p\u003e \u003cp\u003e2.9 Lᵖ Spaces 38\u003c\/p\u003e \u003cp\u003e2.10 Direct Products and Sums 51\u003c\/p\u003e \u003cp\u003e2.11 Schauder Bases 53\u003c\/p\u003e \u003cp\u003e2.12 Fixed Points and Contraction Mappings 53\u003c\/p\u003e \u003cp\u003eExercises 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Major Banach Space Theorems 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 59\u003c\/p\u003e \u003cp\u003e3.2 Baire Category Theorem 59\u003c\/p\u003e \u003cp\u003e3.3 Open Mappings 61\u003c\/p\u003e \u003cp\u003e3.4 Bounded Inverses 63\u003c\/p\u003e \u003cp\u003e3.5 Closed Linear Operators 64\u003c\/p\u003e \u003cp\u003e3.6 Uniform Boundedness Principle 66\u003c\/p\u003e \u003cp\u003eExercises 68\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Hilbert Spaces 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 71\u003c\/p\u003e \u003cp\u003e4.2 Semi-Inner Products 72\u003c\/p\u003e \u003cp\u003e4.3 Nearest Points and Convexity 77\u003c\/p\u003e \u003cp\u003e4.4 Orthogonality 80\u003c\/p\u003e \u003cp\u003e4.5 Linear Functionals on Hilbert Spaces 86\u003c\/p\u003e \u003cp\u003e4.6 Linear Operators on Hilbert Spaces 88\u003c\/p\u003e \u003cp\u003e4.7 Order Relation on Self-Adjoint Operators 97\u003c\/p\u003e \u003cp\u003eExercises 98\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Hahn–Banach Theorem 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 103\u003c\/p\u003e \u003cp\u003e5.2 Basic Version of Hahn–Banach Theorem 104\u003c\/p\u003e \u003cp\u003e5.3 Complex Version of Hahn–Banach Theorem 105\u003c\/p\u003e \u003cp\u003e5.4 Application to Normed Linear Spaces 107\u003c\/p\u003e \u003cp\u003e5.5 Geometric Versions of Hahn–Banach Theorem 108\u003c\/p\u003e \u003cp\u003eExercises 118\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Duality 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Examples of Dual Spaces 121\u003c\/p\u003e \u003cp\u003e6.2 Adjoints 130\u003c\/p\u003e \u003cp\u003e6.3 Double Duals and Reflexivity 133\u003c\/p\u003e \u003cp\u003e6.4 Weak and Weak* Convergence 136\u003c\/p\u003e \u003cp\u003eExercises 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Topological Linear Spaces 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Review of General Topology 143\u003c\/p\u003e \u003cp\u003e7.2 Topologies on Linear Spaces 148\u003c\/p\u003e \u003cp\u003e7.3 Linear Functionals on Topological Linear Spaces 151\u003c\/p\u003e \u003cp\u003e7.4 Weak Topology 153\u003c\/p\u003e \u003cp\u003e7.5 Weak* Topology 156\u003c\/p\u003e \u003cp\u003e7.6 Extreme Points and Krein–Milman Theorem 160\u003c\/p\u003e \u003cp\u003e7.7 Operator Topologies 164\u003c\/p\u003e \u003cp\u003eExercises 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. The Spectrum 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 167\u003c\/p\u003e \u003cp\u003e8.2 Banach Algebras 169\u003c\/p\u003e \u003cp\u003e8.3 General Properties of the Spectrum 170\u003c\/p\u003e \u003cp\u003e8.4 Numerical Range 176\u003c\/p\u003e \u003cp\u003e8.5 Spectrum of a Normal Operator 177\u003c\/p\u003e \u003cp\u003e8.6 Functions of Operators 180\u003c\/p\u003e \u003cp\u003e8.7 Brief Introduction to C_-Algebras 183\u003c\/p\u003e \u003cp\u003eExercises 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Compact Operators 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction and Basic Definitions 187\u003c\/p\u003e \u003cp\u003e9.2 Compactness Criteria in Metric Spaces 188\u003c\/p\u003e \u003cp\u003e9.3 New Compact Operators from Old 192\u003c\/p\u003e \u003cp\u003e9.4 Spectrum of a Compact Operator 194\u003c\/p\u003e \u003cp\u003e9.5 Compact Self-Adjoint Operators on Hilbert Spaces 197\u003c\/p\u003e \u003cp\u003e9.6 Invariant Subspaces 201\u003c\/p\u003e \u003cp\u003eExercises 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Application to Integral and Differential Equations 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 205\u003c\/p\u003e \u003cp\u003e10.2 Integral Operators 206\u003c\/p\u003e \u003cp\u003e10.3 Integral Equations 211\u003c\/p\u003e \u003cp\u003e10.4 Second-Order Linear Differential Equations 214\u003c\/p\u003e \u003cp\u003e10.5 Sturm–Liouville Problems 217\u003c\/p\u003e \u003cp\u003e10.6 First-Order Differential Equations 223\u003c\/p\u003e \u003cp\u003eExercises 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Spectral Theorem for Bounded, Self-Adjoint Operators 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction and Motivation 229\u003c\/p\u003e \u003cp\u003e11.2 Spectral Decomposition 231\u003c\/p\u003e \u003cp\u003e11.3 Extension of Functional Calculus 235\u003c\/p\u003e \u003cp\u003e11.4 Multiplication Operators 240\u003c\/p\u003e \u003cp\u003eExercises 243\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Zorn’s Lemma 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Stone–Weierstrass Theorem 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Basic Theorem 247\u003c\/p\u003e \u003cp\u003eB.2 Nonunital Algebras 250\u003c\/p\u003e \u003cp\u003eB.3 Complex Algebras 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Extended Real Numbers and Limit Points of Sequences 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Extended Reals 253\u003c\/p\u003e \u003cp\u003eC.2 Limit Points of Sequences 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D Measure and Integration 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Introduction and Notation 257\u003c\/p\u003e \u003cp\u003eD.2 Basic Properties of Measures 258\u003c\/p\u003e \u003cp\u003eD.3 Properties of Measurable Functions 259\u003c\/p\u003e \u003cp\u003eD.4 Integral of a Nonnegative Function 261\u003c\/p\u003e \u003cp\u003eD.5 Integral of an Extended Real-Valued Function 265\u003c\/p\u003e \u003cp\u003eD.6 Integral of a Complex-Valued Function 267\u003c\/p\u003e \u003cp\u003eD.7 Construction of Lebesgue Measure on R 267\u003c\/p\u003e \u003cp\u003eD.8 Completeness of Measures 273\u003c\/p\u003e \u003cp\u003eD.9 Signed and Complex Measures 274\u003c\/p\u003e \u003cp\u003eD.10 Radon–Nikodym Derivatives 276\u003c\/p\u003e \u003cp\u003eD.11 Product Measures 278\u003c\/p\u003e \u003cp\u003eD.12 Riesz Representation Theorem 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E Tychonoff’s Theorem 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSymbols 293\u003c\/p\u003e \u003cp\u003eReferences 297\u003c\/p\u003e \u003cp\u003eIndex 299\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402295845207,"sku":"9780470146194","price":116.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470146194.jpg?v=1730479978","url":"https:\/\/bookcurl.com\/products\/a-first-course-in-functional-analysis-9780470146194","provider":"Book Curl","version":"1.0","type":"link"}