Total subset

In mathematics, more specifically in functional analysis, a subset T of a topological vector space X is said to be a total subset of X if the linear span of T is a dense subset of X. 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
• Positive linear operator
• Topological vector spaces

References

• Schaefer, Helmut H. (1999). Topological Vector Spaces. GTM. Vol. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. {{cite book}}: Invalid |ref=harv (help)