In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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
In mathematics, the linear span (also called the linear hull or just span) of a set of vectors (from a vector space), denoted , pp. 29-30, ยงยง 2.5, 2.8 is defined as the set of all linear combinations of the vectors in . It can be characterized ...
of
is a
dense subset of
This condition arises frequently in many theorems of functional analysis.
Examples
Unbounded
self-adjoint operators on
Hilbert space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...
s are defined on total subsets.
See also
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References
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{{Functional analysis
Functional analysis
Topological vector spaces