Analysis Now

1. Front Matter

   Pages i-xiv

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2. General Topology

   • Gert K. Pedersen

   Pages 1-42

3. Banach Spaces

   • Gert K. Pedersen

   Pages 43-78

4. Hilbert Spaces

   • Gert K. Pedersen

   Pages 79-125

5. Spectral Theory

   • Gert K. Pedersen

   Pages 127-189

6. Unbounded Operators

   • Gert K. Pedersen

   Pages 191-219

7. Integration Theory

   • Gert K. Pedersen

   Pages 221-266

8. Back Matter

   Pages 267-280

   PDF

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.

• Gelfand representation
• Hilbert space
• calculus
• compactness
• differential equation
• maximum
• measure
• spectral theorem

G.K. Pedersen

Analysis Now

"The writing is clear and precise, but has an informal and humorous touch which enlivens the material. One of the strengths of the book is the excellent set of problems, which accompany the text."—MATHEMATICAL REVIEWS

• Mathematics Institute, University of Copenhagen, Copenhagen Ø, Denmark

  Gert K. Pedersen

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