CHARACTERIZATION OF THE BEST APPROXIMATION POINTS WITH LATTICE HOMOMORPHISMS
Abstract
In this paper we prove some characterization theorems in the the-
ory of best approximations in Banach lattices. We use a new idea for nding
the best approximation points in an ideal. We nd the distance between an
ideal I and an element x by using lattice homomorphisms. We introduce maxi-
mal ideals of an AM- space and characterize other ideals by the maximal ideals.
Also we give a new representation for principle ideals in Banach lattices that is
a majorizing subspace and we show that these principle ideals are proximinal.
The role of lattice homomorphisms in this paper is very important.
ory of best approximations in Banach lattices. We use a new idea for nding
the best approximation points in an ideal. We nd the distance between an
ideal I and an element x by using lattice homomorphisms. We introduce maxi-
mal ideals of an AM- space and characterize other ideals by the maximal ideals.
Also we give a new representation for principle ideals in Banach lattices that is
a majorizing subspace and we show that these principle ideals are proximinal.
The role of lattice homomorphisms in this paper is very important.
Keywords
Best approximation, ideal, lattice homomorphism, Banach lattice.
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.