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9 - Sequence Spaces

from Part III - Discrete Functional Analysis

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

The study of Sequence Spaces is the basic and natural setting for the study of Functional Analysis. Banach Sequence Spaces with continuous coordinates (K-spaces) are fundamental here. The concepts of Sectional Convergence (AK) and Cesaro Sectional Convergence (SigmaK), as well as more general sectional density (AD), are examined in relation to bv-invariance and q-invariance.

Keywords

K-spacesBK-spacesDual of Sequence SpaceSectional ConvergenceSolid SpacesAK-spacesCesaro Sectional ConvergenceQuasi-convexitybv-invarianceq-invariance
Type
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Information
Classical and Discrete Functional Analysis with Measure Theory , pp. 403 - 425
Publisher: Cambridge University Press
Print publication year: 2022

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  • Sequence Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.014
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  • Sequence Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.014
Available formats
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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.

  • Sequence Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.014
Available formats
×