Kernel of a linear operator
From Encyclopedia of Mathematics
The linear subspace of the domain of definition of the 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 spaces (cf. Locally convex space), 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.
Comments
References
| [a1] | J.L. Kelley, I. Namioka, "Linear topological spaces" , v. Nostrand (1963) pp. Chapt. 5, Sect. 21 |
How to Cite This Entry:
Kernel of a linear operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_linear_operator&oldid=15024
Kernel of a linear operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_linear_operator&oldid=15024
This article was adapted from an original article by G.L. Litvinov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article