Functional Analysis
نویسنده
چکیده
Table of contents: Section 1: Overview, background 1 Section 2: Definition of Banach spaces 2 Section 3: Examples of Banach spaces 2 Section 4: L spaces 6 Section 5: L spaces 9 Section 6: Some spaces that are almost Banach, but aren’t 10 Section 7: Normed vector spaces are metric spaces 11 Section 8: How to make new spaces out of existent ones (or not) 13 Section 9: Finite-dimensional vector spaces are special 18 Section 10: Examples of (infinite dimensional) subspaces 20 Section 11: Sublinear functional and the Hahn–Banach Theorem 22 Section 12: A section of big theorems 27 Section 13: Hilbert spaces 35 Section 14: Perpendicularity 37 Section 15: The Riesz Representation Theorem 41 Section 16: Orthonormal bases 41 Section 17: Section I.5 in the book 46 Section 18: Adjoints of linear transformations 47 Section 19: Self-adjoint operators 49 Section 20: Spectrum 51 Section 21: Holomorphic Banach space-valued functions 55 Appendix A: Some topology facts 59 Appendix B: Homework and exam sets 60
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