Linear Operators on Normed Spaces

  • Kendall Atkinson
  • Weimin Han
Part of the Texts in Applied Mathematics book series (TAM, volume 39)


Many of the basic problems of applied mathematics share the property of linearity, and linear spaces and linear operators provide a general and useful framework for the analysis of such problems. More complicated applications often involve nonlinear operators, and a study of linear operators also offers some useful tools for the analysis of nonlinear operators. In this chapter we review some basic results on linear operators, and we give some illustrative applications to obtain results in numerical analysis. Some of the results are quoted without proof; and usually the reader can find detailed proofs of the results in a standard textbook on functional analysis (e.g., see Conway [40], Kantorovich and Akilov [88], and Zeidler [174, 175]).


Banach Space Linear Operator Kernel Function Integral Operator Normed Space 
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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Kendall Atkinson
    • 1
  • Weimin Han
    • 2
    • 3
  1. 1.Department of Mathematics, Department of Computer ScienceUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA
  3. 3.Department of MathematicsZhejiang UniversityHangzhouPeople’s Republic of China

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