Total subset

Short description: Subset T of a topological vector space X where the linear span of T is a dense subset of X

In mathematics, more specifically in functional analysis, a subset [math]\displaystyle{ T }[/math] of a topological vector space [math]\displaystyle{ X }[/math] is said to be a total subset of [math]\displaystyle{ X }[/math] if the linear span of [math]\displaystyle{ T }[/math] is a dense subset of [math]\displaystyle{ X. }[/math] This condition arises frequently in many theorems of functional analysis.

Examples

Unbounded self-adjoint operators on Hilbert spaces are defined on total subsets.

See also

• Positive linear operator

References

• Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.