Total subset
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 of a topological vector space is said to be a total subset of if the linear span of is a dense subset of [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
- ^ 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.
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