Total subset
Vector space in functional analysis
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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 space
- Positive linear operator – Concept in functional analysis
- Topological vector spaces – Vector space with a notion of nearness
