Transformations of d-Normal Equations
Let equation (A) be d-normal, and let the operator B have a dense domain in F. By Lemma 8.1, one can decompose F as
where dim L = d(A) and L ⊂ D(B). The set of values of the operator B on D(B) is the range R(B), while the set of its values on R(A) ∩ D(B) is the range R(BA) of the operator BA. Since
$$ F = R(A) \oplus L $$
$$ D(B) = R(A) \cap (B) \oplus L $$
$$ R(B) = R(BA) + (BL) $$
KeywordsBanach Space Quotient Space Adjoint Equation Finite Dimensional Space Linear Manifold
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Birkhäuser Boston, Inc. 1982