Chapter 9 Examples of Dual Spaces from Measure Theory

  1. Leonard F. Richardson

Published Online: 29 JUN 2009

DOI: 10.1002/9780470501153.ch9

Measure and Integration: A Concise Introduction to Real Ananysis

Measure and Integration: A Concise Introduction to Real Ananysis

How to Cite

Richardson, L. F. (2009) Chapter 9 Examples of Dual Spaces from Measure Theory, in Measure and Integration: A Concise Introduction to Real Ananysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470501153.ch9

Publication History

  1. Published Online: 29 JUN 2009
  2. Published Print: 17 JUN 2009

ISBN Information

Print ISBN: 9780470259542

Online ISBN: 9780470501153

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Keywords:

  • Banach space;
  • Jensen's inequality;
  • Holder's inequality;
  • Minkowski's inequality;
  • dual of a Banach space;
  • bounded linear functionals;
  • isomorphism;
  • Hilbert space;
  • Hermitian scalar product;
  • Riesz-Markov-Saks-Kakutani theorem

Summary

This chapter contains sections titled:

  • The Banach Space Lp(X, ��, μ)

  • The Dual of a Banach Space

  • The Dual Space of Lp(X, ��, μ)

  • Hilbert Space, Its Dual, and L2(X, ��, μ)

  • Riesz-Markov-Saks-Kakutani Theorem