University of Wisconsin - Madisoncenter for the Mathematical
نویسندگان
چکیده
Given an index set X, a collection IB of subsets of X, and a collection (` x : x 2 X) of commuting linear maps on some linear space, the family of linear operators whose joint kernel K = K(IB) is sought consists of alì A := Q a2Aà with A any subset of X which intersects every B 2 IB. It is shown that certain conditions on IB and`, used in BRS] to obtain the inequality dim K(IB) X B2I B dim K(fBg); or the corresponding equality, can be weakened. For example, the additional assumption of equicar-dinality of the elements of IB used there is dropped. However, the notion of`placeability' introduced in BRS] continues to play an essential role. These results are then described in the rather diierent language employed in (the nal version of) DDM] to facilitate comparisons.
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