We study the theory of best approximation in tensor product and the direct sum of some lattice normed spaces X_{i}. We introduce quasi tensor product space and discuss about the relation between tensor product space and this 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 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.
Iranmanesh, M., & Solimani, F. (2014). BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES. Journal of Algebraic Systems, 2(1), 67-81. doi: 10.22044/jas.2014.303
MLA
M. Iranmanesh; F. Solimani. "BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES", Journal of Algebraic Systems, 2, 1, 2014, 67-81. doi: 10.22044/jas.2014.303
HARVARD
Iranmanesh, M., Solimani, F. (2014). 'BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES', Journal of Algebraic Systems, 2(1), pp. 67-81. doi: 10.22044/jas.2014.303
VANCOUVER
Iranmanesh, M., Solimani, F. BEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES. Journal of Algebraic Systems, 2014; 2(1): 67-81. doi: 10.22044/jas.2014.303
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