Compact Operators and Fredholm Theory

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


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 \(Tx = \lambda x\).


Banach Space Vector Space Linear Algebra Approximation Problem Compact Operator 
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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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