Shahrood University of TechnologyJournal of Algebraic Systems2345-51282120140901BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES678130310.22044/jas.2014.303ENM.IranmaneshDepartment of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.F.SolimaniDepartment of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.Journal Article20130518We study the theory of best approximation in tensor product and the direct sum of some lattice normed spaces<br />X_{i}. We introduce quasi tensor product space and discuss about the relation between tensor product space and this<br />new space which we denote it by X boxtimes Y. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downward or upward and we call them I_{m}-quasi downward or I_{m}-quasi upward.We show that these sets can be interpreted as downward or upward sets. The relation of these sets with<br />downward and upward subsets of the direct sum of lattice normed spaces X_{i} is discussed. This will be done by homomorphism functions. Finally, we introduce the best approximation of these sets.http://jas.shahroodut.ac.ir/article_303_47a2d4b1a718f29bd44bf701d6db4309.pdf