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  • © 2009

Notes on Functional Analysis

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Part of the book series: Texts and Readings in Mathematics (TRM, volume 50)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-ix
  2. Banach Spaces

    • Rajendra Bhatia
    Pages 1-10
  3. Dimensionality

    • Rajendra Bhatia
    Pages 11-18
  4. New Banach Spaces from Old

    • Rajendra Bhatia
    Pages 19-27
  5. The Hahn-Banach Theorem

    • Rajendra Bhatia
    Pages 28-35
  6. The Uniform Boundedness Principle

    • Rajendra Bhatia
    Pages 36-41
  7. The Open Mapping Theorem

    • Rajendra Bhatia
    Pages 42-48
  8. Dual Spaces

    • Rajendra Bhatia
    Pages 49-57
  9. Some Applications

    • Rajendra Bhatia
    Pages 58-65
  10. The Weak Topology

    • Rajendra Bhatia
    Pages 66-72
  11. The Second Dual and the Weak* Topology

    • Rajendra Bhatia
    Pages 73-80
  12. Hilbert Spaces

    • Rajendra Bhatia
    Pages 81-92
  13. Orthonormal Bases

    • Rajendra Bhatia
    Pages 93-102
  14. Linear Operators

    • Rajendra Bhatia
    Pages 103-110
  15. Adjoint Operators

    • Rajendra Bhatia
    Pages 111-118
  16. Some Special Operators in Hilbert Space

    • Rajendra Bhatia
    Pages 119-128
  17. The Resolvent and The Spectrum

    • Rajendra Bhatia
    Pages 129-138
  18. Subdivision of the Spectrum

    • Rajendra Bhatia
    Pages 139-145
  19. Spectra of Normal Operators

    • Rajendra Bhatia
    Pages 146-154
  20. Square Roots and the Polar Decomposition

    • Rajendra Bhatia
    Pages 155-162

About this book

These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The book is organised as twenty six lectures, each corresponding to a ninety minute class session. This may be helpful to teachers planning a course on this topic. Well prepared students can read it on their own.

Authors and Affiliations

  • Indian Statistical Institute, Delhi, India

    Rajendra Bhatia

Bibliographic Information

Buy it now

Buying options

eBook USD 44.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access