Porosity and the bounded linear regularity property
-
Simeon Reich
und
Alexander J. Zaslavski
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
Artikel in diesem Heft
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity
Artikel in diesem Heft
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity
