Operator theory Basic notions: bounded and unbounded operators Concept
Densely defined operator
Summary
A densely defined operator is an unbounded operator whose domain is a dense subspace of the space. Density of the domain is the condition under which the adjoint of an operator on a Hilbert space is well defined. Differential operators on spaces, defined on smooth functions, are the standard examples.
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About this page
| Tag | BCJHNHKQFG |
|---|---|
| URI | m2://BCJHNHKQFG |
| Kind | concept |
| Writing | W0 stub |
| MSC | 47A05, 47B25 |
| Specializes | Unbounded operator |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Spectral theorem for unbounded self-adjoint operators
- Hille–Yosida theorem
- Symmetric operator
- Adjoint of an unbounded operator
- Friedrichs extension
- Lumer–Phillips theorem