Glossary of functional analysis explained

See also: List of functional analysis topics. This is a glossary for the terminology in a mathematical field of functional analysis.

Throughout the article, unless stated otherwise, the base field of a vector space is the field of real numbers or that of complex numbers. Algebras are not assumed to be unital.

See also: List of Banach spaces, glossary of real and complex analysis.

References

• Bourbaki, Espaces vectoriels topologiques
  • • • • M. Takesaki, Theory of Operator Algebras I, Springer, 2001, 2nd printing of the first edition 1979.

Further reading

• Antony Wassermann's lecture notes at http://iml.univ-mrs.fr/~wasserm/
• Jacob Lurie's lecture notes on a von Neumann algebra at https://www.math.ias.edu/~lurie/261y.html
• https://mathoverflow.net/questions/408415/takesaki-theorem-2-6