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Transformations of d-Normal Equations

  • S. G. Krein

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 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
$$ D(B) = R(A) \cap (B) \oplus L $$
(11.2)
we have
$$ R(B) = R(BA) + (BL) $$
.

Keywords

Banach 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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Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

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

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