TY - JOUR T1 - Double-null Operators and the Investigation of Birkhoff's Theorem on Discrete lp Spaces TT - عملگرهای پوچ دوگانه و بررسی قضیۀ بیرکهوف در فضاهای گسسته از نوع lp JF - khu-mmr JO - khu-mmr VL - 6 IS - 3 UR - http://mmr.khu.ac.ir/article-1-2734-en.html Y1 - 2020 SP - 363 EP - 372 KW - Doubly stochastic operator KW - Double-null operator KW - Birkhoff's problem 111 KW - Extreme points N2 - Doubly stochastic matrices play a fundamental role in the theory of majorization. Birkhoff's theorem explains the relation between $ntimes n$ doubly stochastic matrices and permutations. In this paper, we first introduce double-null operators and we will find some important properties of them. Then with the help of double-null operators, we investigate Birkhoff's theorem for descreate $l^p$ spaces../files/site1/files/63/4.pdf M3 10.52547/mmr.6.3.363 ER -