Kernel of a linear operator
The kernel of a continuous linear operator that is defined on a topological vector space is a closed linear subspace of this space. For locally convex spaces, a continuous linear operator has a null kernel (that is, it is a one-to-one mapping of the domain onto the range) if and only if the adjoint operator has a weakly-dense range.
The nullity is the dimension of the kernel.
|[a1]||J.L. Kelley, I. Namioka, "Linear topological spaces" , v. Nostrand (1963) pp. Chapt. 5, Sect. 21|
Kernel of a linear operator. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Kernel_of_a_linear_operator&oldid=36011