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Global Analysis. Studies and Applications III

The implication (i) => (ii) is obvious. From propositions 3. I and 3.4 it immediately
follows that for any a A the equality (son (h)) (a) = 2?h Goh (a)) holds. Hence, (ii)
is equivalent to (iii). From equality (II) we see that [h,h, T. =on (h). Therefore, (iii) ...