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Linear Operators

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc663614
Date12 1900
CreatorsMalhotra, Vijay Kumar
ContributorsLewis, Paul Weldon, Connor, Frank
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatiii, 60 leaves, Text
RightsPublic, Malhotra, Vijay Kumar, Copyright, Copyright is held by the author, unless otherwise noted. All rights

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