Abstract.
H. H. Bauschke and J. M. Borwein showed that in the space of all tuples of bounded, closed, and convex subsets of a Hilbert space with a nonempty intersection, a typical tuple has the bounded linear regularity property. This property is important because it leads to the convergence of infinite products of the corresponding nearest point projections to a point in the intersection. In the present paper we show that the subset of all tuples possessing the bounded linear regularity property has a porous complement. Moreover, our result is established in all normed spaces and for tuples of closed and convex sets, which are not necessarily bounded.
Funding source: Israel Science Foundation
Award Identifier / Grant number: 389/12
Funding source: Fund for the Promotion of Research at the Technion
Funding source: Technion General Research Fund
The authors thank the referees for many helpful comments and suggestions.
© 2014 by Walter de Gruyter Berlin/Boston
