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Normed Spaces and Inner Product Spaces

In: Algebra and Analysis for Engineers and Scientists

Author

Listed:
  • Anthony N. Michel

    (University of Notre Dame, Department of Electrical Engineering)

  • Charles J. Herget

    (Herget Associates)

Abstract

In Chapters 2–4 we concerned ourselves primarily with algebraic aspects of certain mathematical systems, while in Chapter 5 we addressed ourselves to topological properties of some mathematical systems. The stage is now set to combine topological and algebraic structures. In doing so, we arrive at linear topological spaces, namely normed linear spaces and inner product spaces, in general, and Banach spaces and Hilbert spaces, in particular. The properties of such spaces are the topic of the present chapter. In the next chapter we will study linear transformations defined on Banach and Hilbert spaces. The material of the present chapter and the next chapter constitutes part of a branch of mathematics called functional analysis.

Suggested Citation

  • Anthony N. Michel & Charles J. Herget, 2007. "Normed Spaces and Inner Product Spaces," Springer Books, in: Algebra and Analysis for Engineers and Scientists, chapter 6, pages 343-405, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4707-0_6
    DOI: 10.1007/978-0-8176-4707-0_6
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