Linear Transformations of Equations

  • S. G. Krein


By a linear transformation of equation (A) we mean the process of passing from (A) to a new equation
$$ BAx = By $$
by means of a linear operator B which acts from F into a new Banach space G. It could be that the equation
$$ BAx = z $$
is easier to solve than the original one. However, in dealing with such transformations we must proceed with a certain amount of caution. If the operator B is not defined everywhere on F, then the solutions of equation (A) corresponding to right-hand sides y ∉ υ(B) are not in the set of all solutions of equation (BA).


Banach Space Linear Operator Linear Transformation Bounded Operator Bounded Linear Operator 
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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