Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorPedersen, Gert K. author
TitleAnalysis Now [electronic resource] / by Gert K. Pedersen
ImprintNew York, NY : Springer New York : Imprint: Springer, 1989
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1007-8
Descript XIV, 280 p. online resource

SUMMARY

Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view


CONTENT

1 General Topology -- 1.1. Ordered Sets -- 1.2. Topology -- 1.3. Convergence -- 1.4. Continuity -- 1.5. Separation -- 1.6. Compactness -- 1.7. Local Compactness -- 2 Banach Spaces -- 2.1. Normed Spaces -- 2.2. Category -- 2.3. Dual Spaces -- 2.4. Seminormed Spaces -- 2.5. w*-Compactness -- 3 Hilbert Spaces -- 3.1. Inner Products -- 3.2. Operators on Hilbert Space -- 3.3. Compact Operators -- 3.4. The Trace -- 4 Spectral Theory -- 4.1. Banach Algebras -- 4.2. The Gelfand Transform -- 4.3. Function Algebras -- 4.4. The Spectral Theorem, I -- 4.5. The Spectral Theorem, II -- 4.6. Operator Algebra -- 4.7. Maximal Commutative Algebras -- 5 Unbounded Operators -- 5.1. Domains, Extensions, and Graphs -- 5.2. The Cayley Transform -- 5.3. Unlimited Spectral Theory -- 6 Integration Theory -- 6.1. Radon Integrals -- 6.2. Measurability -- 6.3. Measures -- 6.4. LP-Aspaces -- 6.5. Duality Theory -- 6.6. Product Integrals -- List of Symbols


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram