Transformations of d-Normal Equations

Abstract

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

$$ F = R(A) \oplus L $$

((11.1))

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

$$ D(B) = R(A) \cap (B) \oplus L $$

((11.2))

we have

$$ R(B) = R(BA) + (BL) $$

.