closed operator

(redirected from Closed linear 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 ?
Let A be a bounded or closed linear operator in a Banach space X and let f be a X-valued function.
1] for the case where A is a closed linear operator.
where M and N are closed linear operators from a Banach space Y to X.
Even though the case of A being closed can be dealt with using the g-Drazin inverse for closed linear operators in [12], we focus on the bounded case since it has been pointed out in [1-3] that it is enough to consider problem (1) when A is bounded.
Tran, "The Drazin inverse for closed linear operators and the asymptotic convergence of [C.