Linear Vector Spaces

Erdoğan S. Şuhubi
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Erdoğan S. Şuhubi: Yeditepe University, Department of Mathematics

Chapter Chapter II in Functional Analysis, 2003, pp 71-156 from Springer

Abstract: Abstract A set which is equipped with some kind of a structure is customarily called a space. This structure is usually of algebraical and/or geometrical origins — although these notions should be interpreted somewhat differently from the familiar connotations — and help organise the elements of the set into a systematic entirety. This chapter is an introduction to linear vector spaces, or simply linear spaces or vector spaces that are essentially the very foundation on which intricately vast structures of functional analysis can be built systematically by a holistic approach and it aims to reveal and discuss some properties of such spaces induced only by algebraic operations. It is neither possible nor necessary to treat linear vector spaces in their full generality within the framework of this book. We would rather introduce and elaborate some concepts that will be needed in later developments and discuss some interesting results to which they lead.

Keywords: Vector Space; Linear Transformation; Vector Space Versus; Subspace Versus; Cardinal Number (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0141-9_2

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DOI: 10.1007/978-94-017-0141-9_2

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