TY - JOUR
ID - 303
TI - BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Iranmanesh, M.
AU - Solimani, F.
AD - Department of mathematical sciences, Shahrood university of technology, P.O.Box
3619995161-316, Shahrood, Iran.
Y1 - 2014
PY - 2014
VL - 2
IS - 1
SP - 67
EP - 81
KW - Best approximation
KW - proximinal set
KW - downward set
KW - tensor product
KW - quasi tensor product
DO - 10.22044/jas.2014.303
N2 - We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space and discuss about the relation between tensor product space and thisnew 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 withdownward 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.
UR - http://jas.shahroodut.ac.ir/article_303.html
L1 - http://jas.shahroodut.ac.ir/article_303_47a2d4b1a718f29bd44bf701d6db4309.pdf
ER -