closed operator

(redirected from Closable operator)

closed operator

[¦klōzd ′äp·ə‚rād·ər]
(mathematics)
A linear transformation ƒ whose domain A is contained in a normed vector space X satisfying the condition that if lim xn = x for a sequence xn in A, and lim ƒ(xn) = y, then x is in A and ƒ(x) = y.
References in periodicals archive ?
A field operator [phi](f) affiliated to M(D) is said to satisfy an [L.sup.cosh-1] regularity restriction if the strong product [[phi].sub.cosh-1] [(h).sup.1/2] [phi] (f) [[phi].sub.cosh-1] [(h).sup.1/2] is a closable operator for which the closure is [tau]-measurable; that is, the closure is an element of the space [??] (h is the uniquely determined unbounded operator affiliated to M, while [phi] stands for the fundamental function associated with the Orlicz space [L.sup.cosh-1]).
Any closable operator T has a minimal closed extension [bar.T], which is called its closure ([1], section 38).
Furthermore, since the analysis operators happen to be unbounded, we restrict ourselves to closable operators for a minimal controllability on the process.