The phrase "a closed range" is correct and usable in written English.
It can be used in contexts related to mathematics, statistics, or discussions about limits and boundaries.
Example: "The function is defined only within a closed range, ensuring that all values are included."
Alternatives: "a bounded interval" or "a limited range".
Moreover, in [15] the representation of the space X as a direct sum X=mathcal{N}(A)oplus X_{1}=mathcal{R}(A)oplus X_{2}, where M is assumed to have a closed kernel (mathcal{N}(M)) and a closed range (mathcal{R}(M)), and (X_{1}), (X_{2}) are closed subspaces of X, is essential to guarantee a unique strict solution.
The group uses compressed-air guns — known as airsoft guns, which fire tiny plastic pellets — in the training exercises, and sometimes they shoot real guns on a closed range.
Suppose (Ainmathcal{B(H }) has a closed range.
We claim that (C_{psi,varphi}) has a closed range.
There exists h such that (C_{varphi}(h)=g) because (C_{varphi}) has a closed range.
end{aligned} (3.13) So, S is injective and has a closed range.
Corollary 1 in the appendix states that if (mathsf {C}:mathcal {X}rightarrow mathcal {Y}) is a linear operator with closed range, and (mathcal {S}) is a subspace of the range of C, (mathcal {S} subset R(mathsf {C})), then (text {dim} {mathsf {C}}^{leftarrow }(mathcal {S}) = text {dim} N mathsf {C}) + text {dim}(mathcal {S})).
Assume that T is a continuous operator with closed range.
Let (mathcal {X}) and (mathcal {Y}) be Hilbert spaces and let (mathsf {C}:mathcal {X}rightarrow mathcal {Y}) be a linear operator with closed range.
Let (mathcal {X})and (mathcal {Y}) be finite-dimensional Hilbert spaces and let (mathsf {C}:mathcal {X}rightarrow mathcal {Y} be a linear operator with closed range.
All these results lead us to wonder whether there is a equivalence for the compactness of on and on the Bergman-Orlicz space, and whether there is a equivalence for the closed range of on and on the Bergman-Orlicz space.
