ABSTRACT
Theorem 11.6. Let X and Y be two ideal spaces. Then .c;(X,Y) is a closed subspace of .cr (X, Y) which is isomorphic to the space !)leX, Y). More precisely, the two-sided estimate
(11.25) II P II.cr (x,Y) :S lIec, I, m, n)IIlJl(X,Y) :S 4/1PII.cr(x,Y) holds, if P is a regular operator of the form (11.1). o The statement is an immediate consequence of the completeness of the space !)leX, Y) and of Theorems 11.2 and 11.3.•
In view of applications, the following theorem on the superposition of partial integral operators is useful, which follows by a standard reasoning from Fubini's theorem.
