Photosynthetic phosphorylation catalyzed by factors isolated from photosynthetic organisms.

where DaUk converges strongly to Dau in L2(Q). Furthermore, daf(uk)Dv converges strongly to da,,(u)Dv in L2(Q) by dominated convergence. Hence, each term in the sum for a (u k, V) converges to the corresponding term in the sum for a(u, v), (G(uk), v)m . (G(u), v)m for each v in V, and the proof of Lemma 3 is complete. Proof of Theorem 1: By Lemma 2, it suffices to show that the mapping G is oneto-one and onto V. By Lemmas 3 and 1, G is demicontinuous and satisfies the inequality (2.4) of Theorem 4 of Section 2. By that Theorem, G is oneto-one, onto, and has a continuous inverse. QED