View source for Kernel of a linear operator

The linear subspace of the [[domain of definition]] of a [[linear operator]] that consists of all vectors that are mapped to zero. 

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 space]]s, 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.

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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.L. Kelley,   I. Namioka,   "Linear topological spaces" , v. Nostrand  (1963)  pp. Chapt. 5, Sect. 21</TD></TR></table>