Basic Framework

Balmohan V. Limaye ()
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Balmohan V. Limaye: Indian Institute of Technology Bombay, Department of Mathematics

Chapter 2 in Linear Functional Analysis for Scientists and Engineers, 2016, pp 33-74 from Springer

Abstract: Abstract In this chapter, we introduce the structure of a normed space. It involves the superposition of a metric structure on a linear space by means of a norm. Also, we introduce the structure of an inner product space and show that an inner product induces a special kind of norm. We consider the concept of orthogonality in the context of an inner product space. Our study of functional analysis will take place within these basic structures. In the last two sections, we investigate complete normed spaces (which are known as Banach spaces) as well as complete inner product spaces (which are known as Hilbert spaces). We consider many examples of Banach spaces and Hilbert spaces.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0972-3_2

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DOI: 10.1007/978-981-10-0972-3_2

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