678 research outputs found
On the dimension of the set of minimal projections
Let be a finite-dimensional normed space and let be its
proper linear subspace. The set of all minimal projections from to is a
convex subset of the space all linear operators from to and we can
consider its affine dimension. We establish several results on the possible
values of this dimension. We prove optimal upper bounds in terms of the
dimensions of and . Moreover, we improve these estimates in the
polyhedral normed spaces for an open and dense subset of subspaces of the given
dimension. As a consequence, in the polyhedral normed spaces a minimal
projection is unique for an open and dense subset of hyperplanes. To prove
this, we establish certain new properties of the Chalmers-Metcalf operator.
Another consequence is the fact, that for every subspace of a polyhedral normed
space, there exists a minimal projection with many norming pairs. Finally, we
provide some more refined results in the hyperplane case.Comment: 31 page
Conference Program
Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications
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