%0 Journal Article %T NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Gorjizadeh, Farzaneh %A Eftekhari, Noha %D 2024 %\ 01/01/2024 %V 11 %N 2 %P 1-12 %! NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES %K Strong majorization %K Hilbert space‎ %K Positive operator %R 10.22044/jas.2022.11318.1564 %X ‌This work aims to introduce and investigate a preordering in $B(\mathcal{H}),$‌ ‌the Banach space of all bounded linear operators defined on a complex‌ ‌Hilbert space $\mathcal{H}.$ It is called strong majorization and denoted by $S\prec_{s}T,$ for‌ ‌$S,T\in B(\mathcal{H}).$ The strong majorization follows majorization defined by Barnes‌, ‌but not vice versa‌. ‌If $S\prec_{s}T,$ then $S$ inherits some properties of $T.$ ‌‌‌‌ The strong majorization will be extended for the d-tuple of operators in $B(\mathcal{H})^{d}$ and‌ ‌is called joint strong majorization denoted by $S\prec_{js}T,$ for $S,T\in B(\mathcal{H})^{d}.$ We show that‌ ‌some properties of strong majorization are satisfied for joint strong majorization‌. %U https://jas.shahroodut.ac.ir/article_2727_112aa1ae252de4ef66eff1917dd0dc89.pdf