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Here we denote with [[chi].sup.r.sub.k,i] the annihilators of bosons [a.sub.k,i] and the ones of fermions [[alpha].sup.r.sub.k,i] [59, 60].
Let [{[[partial derivative].sub.k]}.sub.k[greater than or equal to] 0] be the Bernoulli annihilators. For a nonnegative function w on N, we first define in the [L.sup.2]-space of Bernoulli functionals a positive, symmetric, densely defined bilinear form [E.sub.w] in the following manner:
is the ij-class of the block Jacobi annihilators. If all [??] are restricted to the class [mathematical expression not reproducible], then the resulting ij-class is denoted by [mathematical expression not reproducible].
And the above theorem holds for p = 2, under the assumption that every element x [member of] R satisfying 2x = 0 is a left or right annihilator of R.
We would like to remark that the same conclusions hold in case we consider the right annihilator, more precisely.
Psychologists who have studied their cases have described them as typical family annihilators.
Lee, Left annihilators characterized by GPI's, Trans.
(46.) See Catharine Skipp, Inside the Minds of Family Annihilators,
The first of them uses the method from [5], the second is based on the formula [H.sub.k+1] = [([H.sub.k] [intersection] [H.sub.k.sup.+).sup.-], for k [greater than or equal to] 1, and the third method computes the sequence of distributions [[DELTA].sub.k] and then finds [H.sub.k+1]'s as their maximal annihilators.
On the Annihilators of Derivations with Engel Conditions in Prime Rings *
Birds are the crop annihilators here, Maragas has found.