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6 - Linear Operators

from Part II - Elements Of Classical Functional Analysis

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

Linear Operators and Linear Functionals are studied. Then Operator Spaces, Topological Duals, and Second Duals of Normed Spaces are considered. Lebesgue L(p) Spaces are defined and studied. The theorems of Hahn–Banach Extension, Baire Category, Riesz Representation, Open Mapping, Closed Graph, and Banach Fixed Points are all proven.

Keywords

Operator SpaceLinear FunctionalsDual SpaceHahn–Banach ExtensionsBaire CategoryUniform BoundednessOpen MappingClosed GraphLebesgue SpacesContraction Maps
Type
Chapter
Information
Classical and Discrete Functional Analysis with Measure Theory , pp. 214 - 252
Publisher: Cambridge University Press
Print publication year: 2022

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  • Linear Operators
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.010
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  • Linear Operators
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.010
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Linear Operators
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.010
Available formats
×