Normed Spaces and Inner Product Spaces

Anthony N. Michel and Charles J. Herget
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Anthony N. Michel: University of Notre Dame, Department of Electrical Engineering
Charles J. Herget: Herget Associates

Chapter 6 in Algebra and Analysis for Engineers and Scientists, 2007, pp 343-405 from Springer

Abstract: 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.

Keywords: Hilbert Space; Banach Space; Linear Space; Normed Space; Linear Subspace (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-0-8176-4707-0_6

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