(3.5) Since K is a compact operator, we can assert that the operator defined by the second term on the right hand side of (3.5) defines a compact operator.
Of course it implies that (beta_{H} C t))=0) (so (C t)) is relatively compact), and then the Mönch fixed point theorem asserts that the operator N possesses fixed points, which means that our evolution problem has (mathcal{L}^{infty} -solutions.
It is easy to see that the existence of solutions to the system of (1) is equivalent to the existence of fixed point of the nonlinear operator T. Therefore it suffices to prove the existence of fixed point of the operator T. To begin with, we assert that the operator T is well defined and (T(P^ subset P^).
Of course it implies that (beta_{H} C t))=0) (so (C t)) is relatively compact) and then the Ascoli type theorem Lemma 5 applies to yield the relative compactness of C. Finally, the Mönch fixed point theorem asserts that the operator N possesses fixed points, which means that our evolution problem has (mathcal{L}^{infty} -solutions.
A similar error would occur in Alex G. Bell's 1978 book, The Machine Plays Chess, which falsely asserted that "the operator was a trained boy (or very small adult) who followed the directions of the chess player who was hidden elsewhere on stage or in the theater…" More books were published about the Turk toward the end of the 20th century.
He asserts that the port operator merely "oversees the coming and going of ships, making sure they are properly loaded and offloaded in the most cost-effective manner".
which asserts that the epsilon operator assigns the same witness to equivalent formulae A and B. For many applications, however, this additional schema is not necessary.
In particular, we prove that in this class of functions the operator-valued corona problem and the completion problem are not equivalent, and establish an Oka-type principle asserting that the completion problem is solvable if and only if it is solvable in the class of continuous operator-valued functions on D with relatively compact images.
His parents have asserted that the camp operators did not recognize the severity of his depression.
Finally, we assert that is an increasing operator.
