CHARACTERIZATION OF THE BEST APPROXIMATION POINTS WITH LATTICE HOMOMORPHISMS

Authors

  • hamid reza khademzadeh Yazd university
  • Hamid Mazaheri Yazd university

DOI:

https://doi.org/10.30495/jme.v8i0.252

Keywords:

Best approximation, ideal, lattice homomorphism, Banach lattice.

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.

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Published

2015-01-05

Issue

Vol. 8

Section

Vol. 8, No. 4, (2014)

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