closability
Closability is a property of linear operators between topological vector spaces, typically between Banach spaces in functional analysis. It concerns whether an operator that is defined on a limited domain can be meaningfully extended to a larger, closed operator using limit processes.
Let T be a linear operator from a domain D(T) in X to Y. T is closable
If T is closable, its closure T̄ is defined on the set of all x for which
Closable operators arise frequently in analysis, especially for unbounded operators. A densely defined operator is closable
See also: closed operator, densely defined operator, adjoint, graph of an operator.