Backward adaptive biorthogonalization.
Ball proximinality of closed * subalgebras in C(Q)
The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that a closed * subalgebra A of C(Q) is strongly ball proximinal in C(Q) and the metric projection from C(Q), onto the closed unit ball of A, is Hausdorff metric continuous and hence has continuous selection.
Ball proximinality of Equable spaces.
Ball remotal subspaces of Banach spaces
We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).
Banach spaces all of whose subspaces have the approximation property
Bernstein's "Lethargy" Theorem in Metrizable Topological Linear Spaces.
Best approximants for bounded functions and the lattice operations.
Best approximants from non-archimedean Stone-Weierstrass subspaces
Best approximation and fixed points in strong -starshaped metric spaces.
Best approximation and strict convexity of metric spaces
Best approximation in Orlicz spaces.
Best approximation in spaces of bounded linear operators [Book]
Best Approximation in the Space of Bounded Operators and its Applications.
Best Approximation In Vector Valued Function Spaces.
Best Approximation with Exponential Orders and Intermediate Spaces.
Best approximations and porous sets
Let be a nonempty compact subset of a Banach space and denote by the family of all nonempty bounded closed convex subsets of . We endow with the Hausdorff metric and show that there exists a set such that its complement is -porous and such that for each and each , the set of solutions of the best approximation problem , , is nonempty and compact, and each minimizing sequence has a convergent subsequence.
Best approximations, fixed points and parametric projections
If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].
Best approximations theorem for a couple in cone Banach space.
Best coapproximation in metric spaces.
Best Coapproximation in Normed Linear Spaces.