Linear Transformations of Equations
By a linear transformation of equation (A) we mean the process of passing from (A) to a new equation
by means of a linear operator B which acts from F into a new Banach space G. It could be that the equation
$$ BAx = By $$
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).
$$ BAx = z $$
KeywordsBanach 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.
Unable to display preview. Download preview PDF.
© Birkhäuser Boston, Inc. 1982