ON ASCERTAINING INDUCTIVELY THE DIMENSION OF THE JOINT KERNEL OF CERTAIN COMMUTING LINEAR-OPERATORS .2.

Given an index set X, a collection B of subsets of X, and a collection (l(x): x epsilon X) of commuting -linear maps on some linear space, t he family of linear operators whose joint kernel K = K(B) is sought co nsists of all l(A) := Pi(a is an element of A) l(a) with A any subset of X which intersects every B is an element of B. It is shown that cer tain conditions on B and l, used in a previous paper to obtain the ine quality dim K(B) less than or equal to (B is an element of B)Sigma dim K({B}), or the corresponding equality, can be weakened. For example, the additional assumption of equicardinality of the elements of B can be dropped. However, the notion of ''placeability'' continues to play an essential role. The results are then described in the rather differ ent language employed by W. Dahmen, A. Dress, and C. A. Micchelli (Adv . in Appl. Math. 17 (1996), 251-307) to facilitate comparisons. (C) 19 96 Academic Press, Inc.