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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.[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
Positive linear operator
Topological vector spaces

References

Schaefer 1999, p. 80.

Schaefer, Helmut H. (1999). Topological Vector Spaces. GTM. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.

Functional analysis (topics – glossary)
Spaces

Hilbert space Banach space Fréchet space topological vector space

Theorems

Hahn–Banach theorem closed graph theorem uniform boundedness principle Kakutani fixed-point theorem Krein–Milman theorem min-max theorem Gelfand–Naimark theorem Banach–Alaoglu theorem

Operators

bounded operator compact operator adjoint operator unitary operator Hilbert–Schmidt operator trace class unbounded operator

Algebras

Banach algebra C*-algebra spectrum of a C*-algebra operator algebra group algebra of a locally compact group von Neumann algebra

Open problems

invariant subspace problem Mahler's conjecture

Applications

Besov space Hardy space spectral theory of ordinary differential equations heat kernel index theorem calculus of variation functional calculus integral operator Jones polynomial topological quantum field theory noncommutative geometry Riemann hypothesis

Advanced topics

locally convex space approximation property balanced set Schwartz space weak topology barrelled space Banach–Mazur distance Tomita–Takesaki theory

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

World

Index

Hellenica World - Scientific Library

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