Shahrood University of TechnologyJournal of Algebraic Systems2345-512811220240101NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES112272710.22044/jas.2022.11318.1564ENFarzaneh GorjizadehDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.Noha EftekhariDepartment of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord,
Iran.Journal Article20211021This work aims to introduce and investigate a preordering in $B(\mathcal{H}),$ <br />the Banach space of all bounded linear operators defined on a complex <br />Hilbert space $\mathcal{H}.$ It is called strong majorization and denoted by $S\prec_{s}T,$ for <br />$S,T\in B(\mathcal{H}).$ The strong majorization follows majorization defined by Barnes, but not vice versa. <br />If $S\prec_{s}T,$ then $S$ inherits some properties of $T.$ <br /> The strong majorization will be extended for the d-tuple of operators in $B(\mathcal{H})^{d}$ and <br />is called joint strong majorization denoted by $S\prec_{js}T,$ for $S,T\in B(\mathcal{H})^{d}.$ We show that <br />some properties of strong majorization are satisfied for joint strong majorization.https://jas.shahroodut.ac.ir/article_2727_112aa1ae252de4ef66eff1917dd0dc89.pdf