Equations with Operators Which Act in a Single Space

  • S. G. Krein


Let A be an operator which acts in the space E, has a domain dense in E, and is Noetherian. The operators A2, A3 ,... enjoy these same properties, and this allows us to introduce a new important characteristic of equation (A). Namely, let W (A) be the set of all elements x such that Akx = θ for some k > 0. This set is a linear manifold: if Ak1x1 = θ and Ak2x2 = θ, then
$$ {A^{k}}\left( {{x_{1}} + {x_{2}}} \right) = \theta {\kern 1pt} for{\kern 1pt} k = \max \left( {{k_{1}},{k_{2}}} \right) $$


Banach Space Compact Operator Homogeneous Equation Basic Notion Adjoint Equation 

Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

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

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