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Closable Operator


A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are sometimes called preclosed (Takesaki 1970), and the extension B of A is sometimes called the closure of A.


See also

Closed Operator, Hilbert Space, Linear Operator, Operator Extension

This entry contributed by Christopher Stover

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References

Loss, M. "About Closed Operators." 2013. http://people.math.gatech.edu/~loss/13Springtea/closedoperators.pdf.Takesaki, M. Tomita's Theory of Modular Hilbert Algebras and its Applications. Berlin: Springer-Verlag, 1970.

Cite this as:

Stover, Christopher. "Closable Operator." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ClosableOperator.html

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