Transformations of d-Normal Equations

  • S. G. Krein


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
$$ F = R(A) \oplus L $$
where dim L = d(A) and LD(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
$$ D(B) = R(A) \cap (B) \oplus L $$
we have
$$ R(B) = R(BA) + (BL) $$


Banach Space Quotient Space Adjoint Equation Finite Dimensional Space Linear Manifold 


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Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

  • S. G. Krein
    • 1
  1. 1.Department of MathematicsVoronezh UniversityVoronezhUSSR

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