## Abstract

As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on then the adjoint equation (A*) is everywhere solvable. To obtaint the estimate (7.1) one need not know for which right-hand sides equation (A) is solvable. Looking from the point of view of the theory of equations, the content of (7.1) is: if x is any solution of equation (A), the it satisfies \( \parallel x{\parallel _E} \leqslant k\parallel y{\parallel _F} \). This is the reason why such estimates are known under the name of

*R*(A), i.e., if one has the estimate$$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$

(7.1)

*a priori estimates*.## Keywords

Banach Space Domain Versus Adjoint Equation Unique Solvability Finite Dimensional Space
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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© Birkhäuser Boston, Inc. 1982