Operator theory Basic notions: bounded and unbounded operators Concept
Closed operator
Summary
A closed operator is an unbounded operator whose graph is a closed subset of the product space. Closedness is the weak substitute for continuity that most differential operators have. On Banach spaces, the closed graph theorem says that a closed operator defined on the whole space is bounded. So interesting closed operators are usually defined on a proper subspace.
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About this page
| Tag | VM7B38PA87 |
|---|---|
| URI | m2://VM7B38PA87 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 47A05, 47B25 |
| Specializes | Unbounded operator |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Von Neumann's theorem on self-adjoint extensions
- Hille–Yosida theorem
- Closable operator
- Closure of an operator
- Adjoint of an unbounded operator
- Spectrum of an operator
- Hellinger–Toeplitz theorem