Total subset

In mathematics, more specifically in functional analysis, a subset ${\displaystyle T}$ of a topological vector space ${\displaystyle X}$ is said to be a total subset of ${\displaystyle X}$ if the linear span of ${\displaystyle T}$ is a dense subset of ${\displaystyle X.}$^[1] 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

• Dense subset – Subset whose closure is the whole spacePages displaying short descriptions of redirect targets
• Positive linear operator – Concept in functional analysis
• Topological vector spaces – Vector space with a notion of nearnessPages displaying short descriptions of redirect targets

References

1. Schaefer & Wolff 1999, p. 80.

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