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List of Banach spaces

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In the mathematical field of functional analysis, Banach spaces are among the most important objects of study. In other areas of mathematical analysis, most spaces which arise in practice turn out to be Banach spaces as well.

Classical Banach spaces

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According to Diestel (1984, Chapter VII), the classical Banach spaces are those defined by Dunford & Schwartz (1958), which is the source for the following table.

Glossary of symbols for the table below:

  • denotes the field of real numbers or complex numbers
  • is a compact Hausdorff space.
  • are real numbers with that are Hölder conjugates, meaning that they satisfy and thus also
  • is a -algebra of sets.
  • is an algebra of sets (for spaces only requiring finite additivity, such as the ba space).
  • is a measure with variation A positive measure is a real-valued positive set function defined on a -algebra which is countably additive.
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Banach spaces in other areas of analysis

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Banach spaces serving as counterexamples

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Notes

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References

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