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Compact Operators and Fredholm Theory

  • Adam BowersEmail author
  • Nigel J. Kalton (deceased)
Chapter
  • 3.5k Downloads
Part of the Universitext book series (UTX)

Abstract

Suppose X is a vector space (over \(\mathbb{R}\) or \(\mathbb{C}\)) and let \(T:X\rightarrow X\) be a linear operator. Let us recall some basic definitions from linear algebra. The kernel (or nullspace) of T is the subspace of X given by \(\mathrm{ker}(T)=\{x:Tx=0\}\). The range (or image) of T is given by \(\mathrm{ran}(T)=\{Tx:x\in X\}\). We say that \(x\in X\) is an eigenvector of T if \(x\neq 0\) and there exists some scalar λ (called an eigenvalue) such that \(Tx = \lambda x\).

Keywords

Banach Space Vector Space Linear Algebra Approximation Problem Compact Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of Missouri, ColumbiaColumbiaUSA

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