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.
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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